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Meta-Analysis – Guide with Definition, Steps & Examples

Published by Owen Ingram at April 26th, 2023 , Revised On April 26, 2023

“A meta-analysis is a formal, epidemiological, quantitative study design that uses statistical methods to generalise the findings of the selected independent studies. “

Meta-analysis and systematic review are the two most authentic strategies in research. When researchers start looking for the best available evidence concerning their research work, they are advised to begin from the top of the evidence pyramid. The evidence available in the form of meta-analysis or systematic reviews addressing important questions is significant in academics because it informs decision-making.

What is Meta-Analysis  

Meta-analysis estimates the absolute effect of individual independent research studies by systematically synthesising or merging the results. Meta-analysis isn’t only about achieving a wider population by combining several smaller studies. It involves systematic methods to evaluate the inconsistencies in participants, variability (also known as heterogeneity), and findings to check how sensitive their findings are to the selected systematic review protocol.   

When Should you Conduct a Meta-Analysis?

Meta-analysis has become a widely-used research method in medical sciences and other fields of work for several reasons. The technique involves summarising the results of independent systematic review studies. 

The Cochrane Handbook explains that “an important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention” (section 10.2).

A researcher or a practitioner should choose meta-analysis when the following outcomes are desirable. 

For generating new hypotheses or ending controversies resulting from different research studies. Quantifying and evaluating the variable results and identifying the extent of conflict in literature through meta-analysis is possible. 

To find research gaps left unfilled and address questions not posed by individual studies. Primary research studies involve specific types of participants and interventions. A review of these studies with variable characteristics and methodologies can allow the researcher to gauge the consistency of findings across a wider range of participants and interventions. With the help of meta-analysis, the reasons for differences in the effect can also be explored. 

To provide convincing evidence. Estimating the effects with a larger sample size and interventions can provide convincing evidence. Many academic studies are based on a very small dataset, so the estimated intervention effects in isolation are not fully reliable.

Elements of a Meta-Analysis

Deeks et al. (2019), Haidilch (2010), and Grant & Booth (2009) explored the characteristics, strengths, and weaknesses of conducting the meta-analysis. They are briefly explained below. 

Characteristics: 

• A systematic review must be completed before conducting the meta-analysis because it provides a summary of the findings of the individual studies synthesised. 
• You can only conduct a meta-analysis by synthesising studies in a systematic review. 
• The studies selected for statistical analysis for the purpose of meta-analysis should be similar in terms of comparison, intervention, and population. 

Strengths: 

• A meta-analysis takes place after the systematic review. The end product is a comprehensive quantitative analysis that is complicated but reliable. 
• It gives more value and weightage to existing studies that do not hold practical value on their own. 
• Policy-makers and academicians cannot base their decisions on individual research studies. Meta-analysis provides them with a complex and solid analysis of evidence to make informed decisions. 

Criticisms: 

• The meta-analysis uses studies exploring similar topics. Finding similar studies for the meta-analysis can be challenging.
• When and if biases in the individual studies or those related to reporting and specific research methodologies are involved, the meta-analysis results could be misleading.

Steps of Conducting the Meta-Analysis 

The process of conducting the meta-analysis has remained a topic of debate among researchers and scientists. However, the following 5-step process is widely accepted. 

Step 1: Research Question

The first step in conducting clinical research involves identifying a research question and proposing a hypothesis . The potential clinical significance of the research question is then explained, and the study design and analytical plan are justified.

Step 2: Systematic Review 

The purpose of a systematic review (SR) is to address a research question by identifying all relevant studies that meet the required quality standards for inclusion. While established journals typically serve as the primary source for identified studies, it is important to also consider unpublished data to avoid publication bias or the exclusion of studies with negative results.

While some meta-analyses may limit their focus to randomized controlled trials (RCTs) for the sake of obtaining the highest quality evidence, other experimental and quasi-experimental studies may be included if they meet the specific inclusion/exclusion criteria established for the review.

Step 3: Data Extraction

After selecting studies for the meta-analysis, researchers extract summary data or outcomes, as well as sample sizes and measures of data variability for both intervention and control groups. The choice of outcome measures depends on the research question and the type of study, and may include numerical or categorical measures.

For instance, numerical means may be used to report differences in scores on a questionnaire or changes in a measurement, such as blood pressure. In contrast, risk measures like odds ratios (OR) or relative risks (RR) are typically used to report differences in the probability of belonging to one category or another, such as vaginal birth versus cesarean birth.

Step 4: Standardisation and Weighting Studies

After gathering all the required data, the fourth step involves computing suitable summary measures from each study for further examination. These measures are typically referred to as Effect Sizes and indicate the difference in average scores between the control and intervention groups. For instance, it could be the variation in blood pressure changes between study participants who used drug X and those who used a placebo.

Since the units of measurement often differ across the included studies, standardization is necessary to create comparable effect size estimates. Standardization is accomplished by determining, for each study, the average score for the intervention group, subtracting the average score for the control group, and dividing the result by the relevant measure of variability in that dataset.

In some cases, the results of certain studies must carry more significance than others. Larger studies, as measured by their sample sizes, are deemed to produce more precise estimates of effect size than smaller studies. Additionally, studies with less variability in data, such as smaller standard deviation or narrower confidence intervals, are typically regarded as higher quality in study design. A weighting statistic that aims to incorporate both of these factors, known as inverse variance, is commonly employed.

Step 5: Absolute Effect Estimation

The ultimate step in conducting a meta-analysis is to choose and utilize an appropriate model for comparing Effect Sizes among diverse studies. Two popular models for this purpose are the Fixed Effects and Random Effects models. The Fixed Effects model relies on the premise that each study is evaluating a common treatment effect, implying that all studies would have estimated the same Effect Size if sample variability were equal across all studies.

Conversely, the Random Effects model posits that the true treatment effects in individual studies may vary from each other, and endeavors to consider this additional source of interstudy variation in Effect Sizes. The existence and magnitude of this latter variability is usually evaluated within the meta-analysis through a test for ‘heterogeneity.’

Forest Plot

The results of a meta-analysis are often visually presented using a “Forest Plot”. This type of plot displays, for each study, included in the analysis, a horizontal line that indicates the standardized Effect Size estimate and 95% confidence interval for the risk ratio used. Figure A provides an example of a hypothetical Forest Plot in which drug X reduces the risk of death in all three studies.

However, the first study was larger than the other two, and as a result, the estimates for the smaller studies were not statistically significant. This is indicated by the lines emanating from their boxes, including the value of 1. The size of the boxes represents the relative weights assigned to each study by the meta-analysis. The combined estimate of the drug’s effect, represented by the diamond, provides a more precise estimate of the drug’s effect, with the diamond indicating both the combined risk ratio estimate and the 95% confidence interval limits.

Figure-A: Hypothetical Forest Plot

Relevance to Practice and Research 

  Evidence Based Nursing commentaries often include recently published systematic reviews and meta-analyses, as they can provide new insights and strengthen recommendations for effective healthcare practices. Additionally, they can identify gaps or limitations in current evidence and guide future research directions.

The quality of the data available for synthesis is a critical factor in the strength of conclusions drawn from meta-analyses, and this is influenced by the quality of individual studies and the systematic review itself. However, meta-analysis cannot overcome issues related to underpowered or poorly designed studies.

Therefore, clinicians may still encounter situations where the evidence is weak or uncertain, and where higher-quality research is required to improve clinical decision-making. While such findings can be frustrating, they remain important for informing practice and highlighting the need for further research to fill gaps in the evidence base.

Methods and Assumptions in Meta-Analysis 

Ensuring the credibility of findings is imperative in all types of research, including meta-analyses. To validate the outcomes of a meta-analysis, the researcher must confirm that the research techniques used were accurate in measuring the intended variables. Typically, researchers establish the validity of a meta-analysis by testing the outcomes for homogeneity or the degree of similarity between the results of the combined studies.

Homogeneity is preferred in meta-analyses as it allows the data to be combined without needing adjustments to suit the study’s requirements. To determine homogeneity, researchers assess heterogeneity, the opposite of homogeneity. Two widely used statistical methods for evaluating heterogeneity in research results are Cochran’s-Q and I-Square, also known as I-2 Index.

Difference Between Meta-Analysis and Systematic Reviews

Meta-analysis and systematic reviews are both research methods used to synthesise evidence from multiple studies on a particular topic. However, there are some key differences between the two.

Systematic reviews involve a comprehensive and structured approach to identifying, selecting, and critically appraising all available evidence relevant to a specific research question. This process involves searching multiple databases, screening the identified studies for relevance and quality, and summarizing the findings in a narrative report.

Meta-analysis, on the other hand, involves using statistical methods to combine and analyze the data from multiple studies, with the aim of producing a quantitative summary of the overall effect size. Meta-analysis requires the studies to be similar enough in terms of their design, methodology, and outcome measures to allow for meaningful comparison and analysis.

Therefore, systematic reviews are broader in scope and summarize the findings of all studies on a topic, while meta-analyses are more focused on producing a quantitative estimate of the effect size of an intervention across multiple studies that meet certain criteria. In some cases, a systematic review may be conducted without a meta-analysis if the studies are too diverse or the quality of the data is not sufficient to allow for statistical pooling.

Software Packages For Meta-Analysis

Meta-analysis can be done through software packages, including free and paid options. One of the most commonly used software packages for meta-analysis is RevMan by the Cochrane Collaboration.

Assessing the Quality of Meta-Analysis 

Assessing the quality of a meta-analysis involves evaluating the methods used to conduct the analysis and the quality of the studies included. Here are some key factors to consider:

• Study selection: The studies included in the meta-analysis should be relevant to the research question and meet predetermined criteria for quality.
• Search strategy: The search strategy should be comprehensive and transparent, including databases and search terms used to identify relevant studies.
• Study quality assessment: The quality of included studies should be assessed using appropriate tools, and this assessment should be reported in the meta-analysis.
• Data extraction: The data extraction process should be systematic and clearly reported, including any discrepancies that arose.
• Analysis methods: The meta-analysis should use appropriate statistical methods to combine the results of the included studies, and these methods should be transparently reported.
• Publication bias: The potential for publication bias should be assessed and reported in the meta-analysis, including any efforts to identify and include unpublished studies.
• Interpretation of results: The results should be interpreted in the context of the study limitations and the overall quality of the evidence.
• Sensitivity analysis: Sensitivity analysis should be conducted to evaluate the impact of study quality, inclusion criteria, and other factors on the overall results.

Overall, a high-quality meta-analysis should be transparent in its methods and clearly report the included studies’ limitations and the evidence’s overall quality.

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Examples of Meta-Analysis

• STANLEY T.D. et JARRELL S.B. (1989), « Meta-regression analysis : a quantitative method of literature surveys », Journal of Economics Surveys, vol. 3, n°2, pp. 161-170.
• DATTA D.K., PINCHES G.E. et NARAYANAN V.K. (1992), « Factors influencing wealth creation from mergers and acquisitions : a meta-analysis », Strategic Management Journal, Vol. 13, pp. 67-84.
• GLASS G. (1983), « Synthesising empirical research : Meta-analysis » in S.A. Ward and L.J. Reed (Eds), Knowledge structure and use : Implications for synthesis and interpretation, Philadelphia : Temple University Press.
• WOLF F.M. (1986), Meta-analysis : Quantitative methods for research synthesis, Sage University Paper n°59.
• HUNTER J.E., SCHMIDT F.L. et JACKSON G.B. (1982), « Meta-analysis : cumulating research findings across studies », Beverly Hills, CA : Sage.

Frequently Asked Questions

What is a meta-analysis in research.

Meta-analysis is a statistical method used to combine results from multiple studies on a specific topic. By pooling data from various sources, meta-analysis can provide a more precise estimate of the effect size of a treatment or intervention and identify areas for future research.

Why is meta-analysis important?

Meta-analysis is important because it combines and summarizes results from multiple studies to provide a more precise and reliable estimate of the effect of a treatment or intervention. This helps clinicians and policymakers make evidence-based decisions and identify areas for further research.

What is an example of a meta-analysis?

A meta-analysis of studies evaluating physical exercise’s effect on depression in adults is an example. Researchers gathered data from 49 studies involving a total of 2669 participants. The studies used different types of exercise and measures of depression, which made it difficult to compare the results.

Through meta-analysis, the researchers calculated an overall effect size and determined that exercise was associated with a statistically significant reduction in depression symptoms. The study also identified that moderate-intensity aerobic exercise, performed three to five times per week, was the most effective. The meta-analysis provided a more comprehensive understanding of the impact of exercise on depression than any single study could provide.

What is the definition of meta-analysis in clinical research?

Meta-analysis in clinical research is a statistical technique that combines data from multiple independent studies on a particular topic to generate a summary or “meta” estimate of the effect of a particular intervention or exposure.

This type of analysis allows researchers to synthesise the results of multiple studies, potentially increasing the statistical power and providing more precise estimates of treatment effects. Meta-analyses are commonly used in clinical research to evaluate the effectiveness and safety of medical interventions and to inform clinical practice guidelines.

Is meta-analysis qualitative or quantitative?

Meta-analysis is a quantitative method used to combine and analyze data from multiple studies. It involves the statistical synthesis of results from individual studies to obtain a pooled estimate of the effect size of a particular intervention or treatment. Therefore, meta-analysis is considered a quantitative approach to research synthesis.

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Descriptive research is carried out to describe current issues, programs, and provides information about the issue through surveys and various fact-finding methods.

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Study Design 101: Meta-Analysis

• Case Report
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• Systematic Review

Meta-Analysis

• Helpful Formulas
• Finding Specific Study Types

A subset of systematic reviews; a method for systematically combining pertinent qualitative and quantitative study data from several selected studies to develop a single conclusion that has greater statistical power. This conclusion is statistically stronger than the analysis of any single study, due to increased numbers of subjects, greater diversity among subjects, or accumulated effects and results.

Meta-analysis would be used for the following purposes:

• To establish statistical significance with studies that have conflicting results
• To develop a more correct estimate of effect magnitude
• To provide a more complex analysis of harms, safety data, and benefits
• To examine subgroups with individual numbers that are not statistically significant

If the individual studies utilized randomized controlled trials (RCT), combining several selected RCT results would be the highest-level of evidence on the evidence hierarchy, followed by systematic reviews, which analyze all available studies on a topic.

• Greater statistical power
• Confirmatory data analysis
• Greater ability to extrapolate to general population affected
• Considered an evidence-based resource

Disadvantages

• Difficult and time consuming to identify appropriate studies
• Not all studies provide adequate data for inclusion and analysis
• Requires advanced statistical techniques
• Heterogeneity of study populations

Design pitfalls to look out for

The studies pooled for review should be similar in type (i.e. all randomized controlled trials).

Are the studies being reviewed all the same type of study or are they a mixture of different types?

The analysis should include published and unpublished results to avoid publication bias.

Does the meta-analysis include any appropriate relevant studies that may have had negative outcomes?

Fictitious Example

Do individuals who wear sunscreen have fewer cases of melanoma than those who do not wear sunscreen? A MEDLINE search was conducted using the terms melanoma, sunscreening agents, and zinc oxide, resulting in 8 randomized controlled studies, each with between 100 and 120 subjects. All of the studies showed a positive effect between wearing sunscreen and reducing the likelihood of melanoma. The subjects from all eight studies (total: 860 subjects) were pooled and statistically analyzed to determine the effect of the relationship between wearing sunscreen and melanoma. This meta-analysis showed a 50% reduction in melanoma diagnosis among sunscreen-wearers.

Real-life Examples

Goyal, A., Elminawy, M., Kerezoudis, P., Lu, V., Yolcu, Y., Alvi, M., & Bydon, M. (2019). Impact of obesity on outcomes following lumbar spine surgery: A systematic review and meta-analysis. Clinical Neurology and Neurosurgery, 177 , 27-36. https://doi.org/10.1016/j.clineuro.2018.12.012

This meta-analysis was interested in determining whether obesity affects the outcome of spinal surgery. Some previous studies have shown higher perioperative morbidity in patients with obesity while other studies have not shown this effect. This study looked at surgical outcomes including "blood loss, operative time, length of stay, complication and reoperation rates and functional outcomes" between patients with and without obesity. A meta-analysis of 32 studies (23,415 patients) was conducted. There were no significant differences for patients undergoing minimally invasive surgery, but patients with obesity who had open surgery had experienced higher blood loss and longer operative times (not clinically meaningful) as well as higher complication and reoperation rates. Further research is needed to explore this issue in patients with morbid obesity.

Nakamura, A., van Der Waerden, J., Melchior, M., Bolze, C., El-Khoury, F., & Pryor, L. (2019). Physical activity during pregnancy and postpartum depression: Systematic review and meta-analysis. Journal of Affective Disorders, 246 , 29-41. https://doi.org/10.1016/j.jad.2018.12.009

This meta-analysis explored whether physical activity during pregnancy prevents postpartum depression. Seventeen studies were included (93,676 women) and analysis showed a "significant reduction in postpartum depression scores in women who were physically active during their pregnancies when compared with inactive women." Possible limitations or moderators of this effect include intensity and frequency of physical activity, type of physical activity, and timepoint in pregnancy (e.g. trimester).

Related Terms

A document often written by a panel that provides a comprehensive review of all relevant studies on a particular clinical or health-related topic/question.

Publication Bias

A phenomenon in which studies with positive results have a better chance of being published, are published earlier, and are published in journals with higher impact factors. Therefore, conclusions based exclusively on published studies can be misleading.

Now test yourself!

1. A Meta-Analysis pools together the sample populations from different studies, such as Randomized Controlled Trials, into one statistical analysis and treats them as one large sample population with one conclusion.

a) True b) False

2. One potential design pitfall of Meta-Analyses that is important to pay attention to is:

a) Whether it is evidence-based. b) If the authors combined studies with conflicting results. c) If the authors appropriately combined studies so they did not compare apples and oranges. d) If the authors used only quantitative data.

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Doing a Meta-Analysis: A Practical, Step-by-Step Guide

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

What is a Meta-Analysis?

Meta-analysis is a statistical procedure used to combine and synthesize findings from multiple independent studies to estimate the average effect size for a particular research question.

Meta-analysis goes beyond traditional narrative reviews by using statistical methods to integrate the results of several studies, leading to a more objective appraisal of the evidence.

This method addresses limitations like small sample sizes in individual studies, providing a more precise estimate of a treatment effect or relationship strength.

Meta-analyses are particularly valuable when individual study results are inconclusive or contradictory, as seen in the example of vitamin D supplementation and the prevention of fractures.

For instance, a meta-analysis published in JAMA in 2017 by Zhao et al. examined 81 randomized controlled trials involving 53,537 participants.

The results of this meta-analysis suggested that vitamin D supplementation was not associated with a lower risk of fractures among community-dwelling adults. This finding contradicted some earlier beliefs and individual study results that had suggested a protective effect.

What’s the difference between a meta-analysis, systematic review, and literature review?

Literature reviews can be conducted without defined procedures for gathering information. Systematic reviews use strict protocols to minimize bias when gathering and evaluating studies, making them more transparent and reproducible.

While a systematic review thoroughly maps out a field of research, it cannot provide unbiased information on the magnitude of an effect. Meta-analysis statistically combines effect sizes of similar studies, going a step further than a systematic review by weighting each study by its precision.

What is Effect Size?

Statistical significance is a poor metric in meta-analysis because it only indicates whether an effect is likely to have occurred by chance. It does not provide information about the magnitude or practical importance of the effect.

While a statistically significant result may indicate an effect different from zero, this effect might be too small to hold practical value. Effect size, on the other hand, offers a standardized measure of the magnitude of the effect, allowing for a more meaningful interpretation of the findings

Meta-analysis goes beyond simply synthesizing effect sizes; it uses these statistics to provide a weighted average effect size from studies addressing similar research questions. The larger the effect size the stronger the relationship between two variables.

If effect sizes are consistent, the analysis demonstrates that the findings are robust across the included studies. When there is variation in effect sizes, researchers should focus on understanding the reasons for this dispersion rather than just reporting a summary effect.

Meta-regression is one method for exploring this variation by examining the relationship between effect sizes and study characteristics.

T here are three primary families of effect sizes used in most meta-analyses:

• Mean difference effect sizes : Used to show the magnitude of the difference between means of groups or conditions, commonly used when comparing a treatment and control group.
• Correlation effect sizes : Represent the degree of association between two continuous measures, indicating the strength and direction of their relationship.
• Odds ratio effect sizes : Used with binary outcomes to compare the odds of an event occurring between two groups, like whether a patient recovers from an illness or not.

The most appropriate effect size family is determined by the nature of the research question and dependent variable. All common effect sizes are able to be transformed from one version to another.

Real-Life Example

Brewin, C. R., Andrews, B., & Valentine, J. D. (2000). Meta-analysis of risk factors for posttraumatic stress disorder in trauma-exposed adults.  Journal of Consulting and Clinical Psychology ,  68 (5), 748.

This meta-analysis of 77 articles examined risk factors for posttraumatic stress disorder (PTSD) in trauma-exposed adults, with sample sizes ranging from 1,149 to over 11,000. Several factors consistently predicted PTSD with small effect sizes (r = 0.10 to 0.19), including female gender, lower education, lower intelligence, previous trauma, childhood adversity, and psychiatric history. Factors occurring during or after trauma showed somewhat stronger effects (r = 0.23 to 0.40), including trauma severity, lack of social support, and additional life stress. Most risk factors did not predict PTSD uniformly across populations and study types, with only psychiatric history, childhood abuse, and family psychiatric history showing homogeneous effects. Notable differences emerged between military and civilian samples, and methodological factors influenced some risk factor effects. The authors concluded that identifying a universal set of pretrauma predictors is premature and called for more research to understand how vulnerability to PTSD varies across populations and contexts.

How to Conduct a Meta-Analysis

Researchers should develop a comprehensive research protocol that outlines the objectives and hypotheses of their meta-analysis.

This document should provide specific details about every stage of the research process, including the methodology for identifying, selecting, and analyzing relevant studies.

For example, the protocol should specify search strategies for relevant studies, including whether the search will encompass unpublished works.

The protocol should be created before beginning the research process to ensure transparency and reproducibility.

Research Protocol

• To estimate the overall effect of growth mindset interventions on the academic achievement of students in primary and secondary school.
• To investigate if the effect of growth mindset interventions on academic achievement differs for students of different ages (e.g., elementary school students vs. high school students).
• To examine if the duration of the growth mindset intervention impacts its effectiveness.
• Growth mindset interventions will have a small, but statistically significant, positive effect on student academic achievement.
• Growth mindset interventions will be more effective for younger students than for older students.
• Longer growth mindset interventions will be more effective than shorter interventions.

Eligibility Criteria

• Published studies in English-language journals.
• Studies must include a quantitative measure of academic achievement (e.g., GPA, course grades, exam scores, or standardized test scores).
• Studies must involve a growth mindset intervention as the primary focus (including control vs treatment group comparison).
• Studies that combine growth mindset training with other interventions (e.g., study skills training, other types of psychological interventions) should be excluded.

Search Strategy

The researchers will search the following databases:

Keywords Combined with Boolean Operators:

• (“growth mindset” OR “implicit theories of intelligence” OR “mindset theory”) AND (“intervention” OR “training” OR “program”) ” OR “educational outcomes”) * OR “pupil ” OR “learner*”)**

Additional Search Strategies:

• Citation Chaining: Examining the reference lists of included studies can uncover additional relevant articles.
• Contacting Experts: Reaching out to researchers in the field of growth mindset can reveal unpublished studies or ongoing research.

Coding of Studies

The researchers will code each study for the following information:

• Sample size
• Age of participants
• Duration of intervention
• Type of academic outcome measured
• Study design (e.g., randomized controlled trial, quasi-experiment)

Statistical Analysis

• The researchers will calculate an effect size (e.g., standardized mean difference) for each study.
• The researchers will use a random-effects model to account for variation in effect sizes across studies.
• The researchers will use meta-regression to test the hypotheses about moderators of the effect of growth mindset interventions.

PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) is a reporting guideline designed to improve the transparency and completeness of systematic review reporting.

PRISMA was created to tackle the issue of inadequate reporting often found in systematic reviews

• Checklist : PRISMA features a 27-item checklist covering all aspects of a meta-analysis, from the rationale and objectives to the synthesis of findings and discussion of limitations. Each checklist item is accompanied by detailed reporting recommendations in an Explanation and Elaboration document .
• Flow Diagram : PRISMA also includes a flow diagram to visually represent the study selection process, offering a clear, standardized way to illustrate how researchers arrived at the final set of included studies

Step 1: Defining a Research Question

A well-defined research question is a fundamental starting point for any research synthesis. The research question should guide decisions about which studies to include in the meta-analysis, and which statistical model is most appropriate.

For example:

• How do dysfunctional attitudes and negative automatic thinking directly and indirectly impact depression?
• Do growth mindset interventions generally improve students’ academic achievement?
• What is the association between child-parent attachment and prosociality in children?
• What is the relation of various risk factors to Post Traumatic Stress Disorder (PTSD)?

Step 2: Search Strategy

Present the full search strategies for all databases, registers and websites, including any filters and limits used. PRISMA 2020 Checklist

A search strategy is a comprehensive and reproducible plan for identifying all relevant research studies that address a specific research question.

This systematic approach to searching helps minimize bias.

It’s important to be transparent about the search strategy and document all decisions for auditability. The goal is to identify all potentially relevant studies for consideration.

PRISMA  (Preferred Reporting Items for Systematic reviews and Meta-Analyses) provide appropriate guidance for reporting quantitative literature searches.

Information Sources

The primary goal is to find all published and unpublished studies that meet the predefined criteria of the research question. This includes considering various sources beyond typical databases

Information sources for a meta-analysis can include a wide range of resources like scholarly databases, unpublished literature, conference papers, books, and even expert consultations.

Specify all databases, registers, websites, organisations, reference lists and other sources searched or consulted to identify studies. Specify the date when each source was last searched or consulted. PRISMA 2020 Checklist

An exhaustive, systematic search strategy is developed with the assistance of an expert librarian.

• Databases:  Searches should include seven key databases: CINAHL, Medline, APA PsycArticles, Psychology and Behavioral Sciences Collection, APA PsycInfo, SocINDEX with Full Text, and Web of Science: Core Collections.
• Grey Literature : In addition to databases, forensic or ‘expansive’ searches can be conducted. This includes: grey literature database searches (e.g.  OpenGrey , WorldCat , Ethos ),  conference proceedings, unpublished reports, theses  , clinical trial databases , searches by names of authors of relevant publications. Independent research bodies may also be good sources of material, e.g. Centre for Research in Ethnic Relations , Joseph Rowntree Foundation , Carers UK .
• Citation Searching : Reference lists often lead to highly cited and influential papers in the field, providing valuable context and background information for the review.
• Contacting Experts: Reaching out to researchers or experts in the field can provide access to unpublished data or ongoing research not yet publicly available.

It is important to note that this may not be an exhaustive list of all potential databases.

Search String Construction

It is recommended to consult topic experts on the review team and advisory board in order to create as complete a list of search terms as possible for each concept.

To retrieve the most relevant results, a search string is used. This string is made up of:

• Keywords:  Search terms should be relevant to the research questions, key variables, participants, and research design. Searches should include indexed terms, titles, and abstracts. Additionally, each database has specific indexed terms, so a targeted search strategy must be created for each database.
• Synonyms: These are words or phrases with similar meanings to the keywords, as authors may use different terms to describe the same concepts. Including synonyms helps cover variations in terminology and increases the chances of finding all relevant studies. For example, a drug intervention may be referred to by its generic name or by one of its several proprietary names.
• Truncation symbols : These broaden the search by capturing variations of a keyword. They function by locating every word that begins with a specific root. For example, if a user was researching interventions for smoking, they might use a truncation symbol to search for “smok*” to retrieve records with the words “smoke,” “smoker,” “smoking,” or “smokes.” This can save time and effort by eliminating the need to input every variation of a word into a database.
• Boolean operators: The use of Boolean operators (AND/OR/NEAR/NOT) helps to combine these terms effectively, ensuring that the search strategy is both sensitive and specific. For instance, using “AND” narrows the search to include only results containing both terms, while “OR” expands it to include results containing either term.

When conducting these searches, it is important to combine browsing of texts (publications) with periods of more focused systematic searching. This iterative process allows the search to evolve as the review progresses.

It is important to note that this information may not be entirely comprehensive and up-to-date.

Studies were identified by searching PubMed, PsycINFO, and the Cochrane Library. We conducted searches for studies published between the first available year and April 1, 2009, using the search term mindfulness combined with the terms meditation, program, therapy, or intervention and anxi , depress , mood, or stress. Additionally, an extensive manual review was conducted of reference lists of relevant studies and review articles extracted from the database searches. Articles determined to be related to the topic of mindfulness were selected for further examination.

Specify the inclusion and exclusion criteria for the review. PRISMA 2020 Checklist

Before beginning the literature search, researchers should establish clear eligibility criteria for study inclusion

To maintain transparency and minimize bias, eligibility criteria for study inclusion should be established a priori. Ideally, researchers should aim to include only high-quality randomized controlled trials that adhere to the intention-to-treat principle.

The selection of studies should not be arbitrary, and the rationale behind inclusion and exclusion criteria should be clearly articulated in the research protocol.

When specifying the inclusion and exclusion criteria, consider the following aspects:

• Intervention Characteristics: Researchers might decide that, in order to be included in the review, an intervention must have specific characteristics. They might require the intervention to last for a certain length of time, or they might determine that only interventions with a specific theoretical basis are appropriate for their review.
• Population Characteristics: A meta-analysis might focus on the effects of an intervention for a specific population. For instance, researchers might choose to focus on studies that included only nurses or physicians.
• Outcome Measures: Researchers might choose to include only studies that used outcome measures that met a specific standard.
• Age of Participants: If a meta-analysis is examining the effects of a treatment or intervention for children, the authors of the review will likely choose to exclude any studies that did not include children in the target age range.
• Diagnostic Status of Participants: Researchers conducting a meta-analysis of treatments for anxiety will likely exclude any studies where the participants were not diagnosed with an anxiety disorder.
• Study Design: Researchers might determine that only studies that used a particular research design, such as a randomized controlled trial, will be included in the review.
• Control Group: In a meta-analysis of an intervention, researchers might choose to include only studies that included certain types of control groups, such as a waiting list control or another type of intervention.
• Publication status : Decide whether only published studies will be included or if unpublished works, such as dissertations or conference proceedings, will also be considered.

Studies were selected if (a) they included a mindfulness-based intervention, (b) they included a clinical sample (i.e., participants had a diagnosable psychological or physical/medical disorder), (c) they included adult samples (18 – 65 years of age), (d) the mindfulness program was not coupled with treatment using acceptance and commitment therapy or dialectical behavior therapy, (e) they included a measure of anxiety and/or mood symptoms at both pre and postintervention, and (f) they provided sufficient data to perform effect size analyses (i.e., means and standard deviations, t or F values, change scores, frequencies, or probability levels). Studies were excluded if the sample overlapped either partially or completely with the sample of another study meeting inclusion criteria for the meta-analysis. In these cases, we selected for inclusion the study with the larger sample size or more complete data for measures of anxiety and depression symptoms. For studies that provided insufficient data but were otherwise appropriate for the analyses, authors were contacted for supplementary data.

Iterative Process

The iterative nature of developing a search strategy stems from the need to refine and adapt the search process based on the information encountered at each stage.

A single attempt rarely yields the perfect final strategy. Instead, it is an evolving process involving a series of test searches, analysis of results, and discussions among the review team.

Here’s how the iterative process unfolds:

• Initial Strategy Formulation: Based on the research question, the team develops a preliminary search strategy, including identifying relevant keywords, synonyms, databases, and search limits.
• Test Searches and Refinement: The initial search strategy is then tested on chosen databases. The results are reviewed for relevance, and the search strategy is refined accordingly. This might involve adding or modifying keywords, adjusting Boolean operators, or reconsidering the databases used.
• Discussions and Iteration: The search results and proposed refinements are discussed within the review team. The team collaboratively decides on the best modifications to improve the search’s comprehensiveness and relevance.
• Repeating the Cycle: This cycle of test searches, analysis, discussions, and refinements is repeated until the team is satisfied with the strategy’s ability to capture all relevant studies while minimizing irrelevant results.

By constantly refining the search strategy based on the results and feedback, researchers can be more confident that they have identified all relevant studies.

This iterative process ensures that the applied search strategy is sensitive enough to capture all relevant studies while maintaining a manageable scope.

Throughout this process, meticulous documentation of the search strategy, including any modifications, is crucial for transparency and future replication of the meta-analysis.

Step 3: Search the Literature

Conduct a systematic search of the literature using clearly defined search terms and databases.

Applying the search strategy involves entering the constructed search strings into the respective databases’ search interfaces. These search strings, crafted using Boolean operators, truncation symbols, wildcards, and database-specific syntax, aim to retrieve all potentially relevant studies addressing the research question.

The researcher, during this stage, interacts with the database’s features to refine the search and manage the retrieved results.

This might involve employing search filters provided by the database to focus on specific study designs, publication types, or other relevant parameters.

Applying the search strategy is not merely a mechanical process of inputting terms; it demands a thorough understanding of database functionalities and a discerning eye to adjust the search based on the nature of retrieved results.

Step 4: Screening & Selecting Research Articles

Once the literature search is complete, the next step is to screen and select the studies that will be included in the meta-analysis.

This involves carefully reviewing each study to determine its relevance to the research question and its methodological quality.

The goal is to identify studies that are both relevant to the research question and of sufficient quality to contribute to a meaningful synthesis.

Studies meeting the eligibility criteria are usually saved into electronic databases, such as Endnote or Mendeley , and include title, authors, date and publication journal along with an abstract (if available).

Selection Process

Specify the methods used to decide whether a study met the inclusion criteria of the review, including how many reviewers screened each record and each report retrieved, whether they worked independently, and if applicable, details of automation tools used in the process. PRISMA 2020 Checklist

The selection process in a meta-analysis involves multiple reviewers to ensure rigor and reliability.

Two reviewers should independently screen titles and abstracts, removing duplicates and irrelevant studies based on predefined inclusion and exclusion criteria.

• Initial screening of titles and abstracts: After applying a strategy to search the literature,, the next step involves screening the titles and abstracts of the identified articles against the predefined inclusion and exclusion criteria. During this initial screening, reviewers aim to identify potentially relevant studies while excluding those clearly outside the scope of the review. It is crucial to prioritize over-inclusion at this stage, meaning that reviewers should err on the side of keeping studies even if there is uncertainty about their relevance. This cautious approach helps minimize the risk of inadvertently excluding potentially valuable studies.
• Retrieving and assessing full texts: For studies which a definitive decision cannot be made based on the title and abstract alone, reviewers need to obtain the full text of the articles for a comprehensive assessment against the predefined inclusion and exclusion criteria. This stage involves meticulously reviewing the full text of each potentially relevant study to determine its eligibility definitively.
• Resolution of Disagreements : In cases of disagreement between reviewers regarding a study’s eligibility, a predefined strategy involving consensus-building discussions or arbitration by a third reviewer should be in place to reach a final decision. This collaborative approach ensures a fair and impartial selection process, further strengthening the review’s reliability.

PRISMA Flowchart

The PRISMA flowchart is a visual representation of the study selection process within a systematic review.

The flowchart illustrates the step-by-step process of screening, filtering, and selecting studies based on predefined inclusion and exclusion criteria.

The flowchart visually depicts the following stages:

• Identification: The initial number of titles and abstracts identified through database searches.
• Screening: The screening process, based on titles and abstracts.
• Eligibility: Full-text copies of the remaining records are retrieved and assessed for eligibility.
• Inclusion: Applying the predefined inclusion criteria resulted in the inclusion of publications that met all the criteria for the review.
• Exclusion: The flowchart details the reasons for excluding the remaining records.

This systematic and transparent approach, as visualized in the PRISMA flowchart, ensures a robust and unbiased selection process, enhancing the reliability of the systematic review’s findings.

The flowchart serves as a visual record of the decisions made during the study selection process, allowing readers to assess the rigor and comprehensiveness of the review.

• How to fill a PRISMA flow diagram

Step 5: Evaluating the Quality of Studies

Data collection process.

Specify the methods used to collect data from reports, including how many reviewers collected data from each report, whether they worked independently, any processes for obtaining or confirming data from study investigators, and if applicable, details of automation tools used in the process. PRISMA 2020 Checklist

Data extraction focuses on information relevant to the research question, such as risk or recovery factors related to a particular phenomenon.

Extract data relevant to the research question, such as effect sizes, sample sizes, means, standard deviations, and other statistical measures.

It can be useful to focus on the authors’ interpretations of findings rather than individual participant quotes, as the latter lacks the full context of the original data.

The coding of studies in a meta-analysis involves carefully and systematically extracting data from each included study in a standardized and reliable manner. This step is essential for ensuring the accuracy and validity of the meta-analysis’s findings.

This information is then used to calculate effect sizes, examine potential moderators, and draw overall conclusions.

Coding procedures typically involve creating a standardized record form or coding protocol. This form guides the extraction of data from each study in a consistent and organized manner. Two independent observers can help to ensure accuracy and minimize errors during data extraction.

Beyond basic information like authors and publication year, code crucial study characteristics relevant to the research question.

For example, if the meta-analysis focuses on the effects of a specific therapy, relevant characteristics to code might include:

• Study characteristics : Publicatrion year, authors, country of origin, publication status ( Published : Peer-reviewed journal articles and book chapters Unpublished : Government reports, websites, theses/dissertations, conference presentations, unpublished manuscripts).
• Intervention : Type (e.g., CBT), duration of treatment, frequency (e.g., weekly sessions), delivery method (e.g., individual, group, online), intention-to-treat analysis (Yes/No)
• Outcome measures : Primary vs. secondary outcomes, time points of measurement (e.g., post-treatment, follow-up).
• Moderators : Participant characteristics that might moderate the effect size. (e.g., age, gender, diagnosis, socioeconomic status, education level, comorbidities).
• Study design : Design (RCT quasi-experiment, etc.), blinding, control group used (e.g., waitlist control, treatment as usual), study setting (clinical, community, online/remote, inpatient vs. outpatient), pre-registration (yes/no), allocation method (simple randomization, block randomization, etc.).
• Sample : Recruitment method (snowball, random, etc.), sample size (total and groups), sample location (treatment & control group), attrition rate, overlap with sample(s) from another study?
• Adherence to reporting guidelines : e.g., CONSORT, STROBE, PRISMA
• Funding source : Government, industry, non-profit, etc.
• Effect Size : Comprehensive meta-analysis program is used to compute d and/or r. Include up to 3 digits after the decimal point for effect size information and internal consistency information. Also record the page number and table number from which the information is coded. This information helps when checking reliability and accuracy to ensure we are coding from the same information.

Before applying the coding protocol to all studies, it’s crucial to pilot test it on a small subset of studies. This helps identify any ambiguities, inconsistencies, or areas for improvement in the coding protocol before full-scale coding begins.

It’s common to encounter missing data in primary research articles. Develop a clear strategy for handling missing data, which might involve contacting study authors, using imputation methods, or performing sensitivity analyses to assess the impact of missing data on the overall results.

Quality Appraisal Tools

Researchers use standardized tools to assess the quality and risk of bias in the quantitative studies included in the meta-analysis. Some commonly used tools include:

• Recommended by the Cochrane Collaboration for assessing randomized controlled trials (RCTs).
• Evaluates potential biases in selection, performance, detection, attrition, and reporting.
• Used for assessing the quality of non-randomized studies, including case-control and cohort studies.
• Evaluates selection, comparability, and outcome assessment.
• Assesses risk of bias in non-randomized studies of interventions.
• Evaluates confounding, selection bias, classification of interventions, deviations from intended interventions, missing data, measurement of outcomes, and selection of reported results.
• Specifically designed for diagnostic accuracy studies.
• Assesses risk of bias and applicability concerns in patient selection, index test, reference standard, and flow and timing.

By using these tools, researchers can ensure that the studies included in their meta-analysis are of high methodological quality and contribute reliable quantitative data to the overall analysis.

Step 6: Choice of Effect Size

The choice of effect size metric is typically determined by the research question and the nature of the dependent variable.

• Odds Ratio (OR) : For instance, if researchers are working in medical and health sciences where binary outcomes are common (e.g., yes/no, failed/success), effect sizes like relative risk and odds ratio are often used.
• Mean Difference : Studies focusing on experimental or between-group comparisons often employ mean differences. The raw mean difference, or unstandardized mean difference, is suitable when the scale of measurement is inherently meaningful and comparable across studies.
• Standardized Mean Difference (SMD) : If studies use different scales or measures, the standardized mean difference (e.g., Cohen’s d) is more appropriate. When analyzing observational studies, the correlation coefficient is commonly chosen as the effect size.
• Pearson correlation coefficient (r) : A statistical measure frequently employed in meta-analysis to examine the strength of the relationship between two continuous variables.

Conversion of efect sizes to a common measure

May be necessary to convert reported findings to the chosen primary effect size. The goal is to harmonize different effect size measures to a common metric for meaningful comparison and analysis.

This conversion allows researchers to include studies that report findings using various effect size metrics. For instance, r can be approximately converted to d, and vice versa, using specific equations. Similarly, r can be derived from an odds ratio using another formula.

Many equations relevant to converting effect sizes can be found in Rosenthal (1991).

Step 7: Assessing Heterogeneity

Heterogeneity refers to the variation in effect sizes across studies after accounting for within-study sampling errors.

Heterogeneity refers to how much the results (effect sizes) vary between different studies, where no variation would mean all studies showed the same improvement (no heterogeneity), while greater variation indicates more heterogeneity.

Assessing heterogeneity matters because it helps us understand if the study intervention works consistently across different contexts and guides how we combine and interpret the results of multiple studies.

While little heterogeneity allows us to be more confident in our overall conclusion, significant heterogeneity necessitates further investigation into its underlying causes.

How to assess heterogeneity

• Homogeneity Test : Meta-analyses typically include a homogeneity test to determine if the effect sizes are estimating the same population parameter. The test statistic, denoted as Q, is a weighted sum of squares that follows a chi-square distribution. A significant Q statistic suggests that the effect sizes are heterogeneous.
• I2 Statistic : The I2 statistic is a relative measure of heterogeneity that represents the ratio of between-study variance (τ2) to the total variance (between-study variance plus within-study variance). Higher I2 values indicate greater heterogeneity.
• Prediction Interval : Examining the width of a prediction interval can provide insights into the degree of heterogeneity. A wide prediction interval suggests substantial heterogeneity in the population effect size.

Step 8: Choosing the Meta-Analytic Model

Meta-analysts address heterogeneity by choosing between fixed-effects and random-effects analytical models.

Use a random-effects model if heterogeneity is high. Use a fixed-effect model if heterogeneity is low, or if all studies are functionally identical and you are not seeking to generalize to a range of scenarios.

Although a statistical test for homogeneity can help assess the variability in effect sizes across studies, it shouldn’t dictate the choice between fixed and random effects models.

The decision of which model to use is ultimately a conceptual one, driven by the researcher’s understanding of the research field and the goals of the meta-analysis.

If the number of studies is limited, a fixed-effects analysis is more appropriate, while more studies are required for a stable estimate of the between-study variance in a random-effects model.

It is important to note that using a random-effects model is generally a more conservative approach.

Fixed-effects models

• Assumes all studies are measuring the exact same thing
• Gives much more weight to larger studies
• Use when studies are very similar

Fixed-effects models assume that there is one true effect size underlying all studies. The goal is to estimate this common effect size with the greatest precision, which is achieved by minimizing the within-study (sampling).

Consequently, studies are weighted by the inverse of their variance.

This means that larger studies, which generally have smaller variances, are assigned greater weight in the analysis because they provide more precise estimates of the common effect size

• Simplicity: The fixed-effect model is straightforward to implement and interpret, making it computationally simpler.
• Precision: When the assumption of a common effect size is met, fixed-effect models provide more precise estimates with narrower confidence intervals compared to random-effects models.
• Suitable for Conditional Inferences: Fixed-effect models are appropriate when the goal is to make inferences specifically about the studies included in the meta-analysis, without generalizing to a broader population.
• Restrictive Assumptions: The fixed-effect model assumes all studies estimate the same population parameter, which is often unrealistic, particularly with studies drawn from diverse methodologies or populations.
• Limited Generalizability: Findings from fixed-effect models are conditional on the included studies, limiting their generalizability to other contexts or populations.
• Sensitivity to Heterogeneity: Fixed-effect models are sensitive to the presence of heterogeneity among studies, and may produce misleading results if substantial heterogeneity exists.

Random-effects models

• Assumes studies might be measuring slightly different things
• Gives more balanced weight to both large and small studies
• Use when studies might vary in methods or populations

Random-effects models assume that the true effect size can vary across studies. The goal here is to estimate the mean of these varying effect sizes, considering both within-study variance and between-study variance (heterogeneity).

This approach acknowledges that each study might estimate a slightly different effect size due to factors beyond sampling error, such as variations in study populations, interventions, or designs.

This balanced weighting prevents large studies from disproportionately influencing the overall effect size estimate, leading to a more representative average effect size that reflects the distribution of effects across a range of studies.

• Realistic Assumptions: Random-effects models acknowledge the presence of between-study variability by assuming true effects are randomly distributed, making it more suitable for real-world research scenarios.
• Generalizability: Random-effects models allow for broader inferences to be made about a population of studies, enhancing the generalizability of findings.
• Accommodation of Heterogeneity: Random-effects models explicitly model heterogeneity, providing a more accurate representation of the overall effect when studies have varying effect sizes.
• Complexity: Random-effects models are computationally more complex, requiring the estimation of additional parameters, such as between-study variance.
• Reduced Precision: Confidence intervals tend to be wider compared to fixed-effect models, particularly when between-study heterogeneity is substantial.
• Requirement for Sufficient Studies: Accurate estimation of between-study variance necessitates a sufficient number of studies, making random-effects models less reliable with smaller meta-analyses.

Step 9: Perform the Meta-Analysis

This step involves statistically combining effect sizes from chosen studies. Meta-analysis uses the weighted mean of effect sizes, typically giving larger weights to more precise studies (often those with larger sample sizes).

The main function of meta-analysis is to estimate effects in a population by combining the effect sizes from multiple articles.

It uses a weighted mean of the effect sizes, typically giving larger weights to more precise studies, often those with larger sample sizes.

This weighting scheme makes statistical sense because an effect size with good sampling accuracy (i.e., likely to be an accurate reflection of reality) is weighted highly.

On the other hand, effect sizes from studies with lower sampling accuracy are given less weight in the calculations.

the process:

• Calculate weights for each study
• Multiply each study’s effect by its weight
• Add up all these weighted effects
• Divide by the sum of all weights

Estimating effect size using fixed effects

The fixed-effects model in meta-analysis operates under the assumption that all included studies are estimating the same true effect size.

This model focuses solely on within-study variance when determining the weight of each study.

The weight is calculated as the inverse of the within-study variance, which typically results in larger studies receiving substantially more weight in the analysis.

This approach is based on the idea that larger studies provide more precise estimates of the true effect.

The weighted mean effect size (M) is calculated by summing the products of each study’s effect size (ESi) and its corresponding weight (wi) and dividing that sum by the total sum of the weights:

1. Calculate weights (wi) for each study:

The weight is often the inverse of the variance of the effect size. This means studies with larger sample sizes and less variability will have greater weight, as they provide more precise estimates of the effect size

This weighting scheme reflects the assumption in a fixed-effect model that all studies are estimating the same true effect size, and any observed differences in effect sizes are solely due to sampling error. Therefore, studies with less sampling error (i.e., smaller variances) are considered more reliable and are given more weight in the analysis.

Here’s the formula for calculating the weight in a fixed-effect meta-analysis:

Wi = 1 / VYi 1

• Wi represents the weight assigned to study i.
• VYi is the within-study variance for study i.

Practical steps:

• The weight for each study is calculated as: Weight = 1 / (within-study variance)
• For example: Let’s say a study reports a within-study variance of 0.04. The weight for this study would be: 1 / 0.04 = 25
• Calculate the weight for every study included in your meta-analysis using this method.
• These weights will be used in subsequent calculations, such as computing the weighted mean effect size.
• Note : In a fixed-effects model, we do not calculate or use τ² (tau squared), which represents between-study variance. This is only used in random-effects models.

2. Multiply each study’s effect by its weight:

After calculating the weight for each study, multiply the effect size by its corresponding weight. This step is crucial because it ensures that studies with more precise effect size estimates contribute proportionally more to the overall weighted mean effect size

• For each study, multiply its effect size by the weight we just calculated.

3. Add up all these weighted effects:

Sum up all the products from step 2.

4. Divide by the sum of all weights:

• Add up all the weights we calculated in step 1.
• Divide the sum from step 3 by this total weight.

Implications of the fixed-effects model

• Larger studies (with smaller within-study variance) receive substantially more weight.
• This model assumes that differences between study results are due only to sampling error.
• It’s most appropriate when studies are very similar in methods and sample characteristics.

Estimating effect size using random effects

Random effects meta-analysis is slightly more complicated because multiple sources of differences potentially affecting effect sizes must be accounted for.

The main difference in the random effects model is the inclusion of τ² (tau squared) in the weight calculation. This accounts for between-study heterogeneity, recognizing that studies might be measuring slightly different effects.

This process results in an overall effect size that takes into account both within-study and between-study variability, making it more appropriate when studies differ in methods or populations.

The model estimates the variance of the true effect sizes (τ²). This requires a reasonable number of studies, so random effects estimation might not be feasible with very few studies.

Estimation is typically done using statistical software, with restricted maximum likelihood (REML) being a common method.

1. Calculate weights for each study:

In a random-effects meta-analysis, the weight assigned to each study (W*i) is calculated as the inverse of that study’s variance, similar to a fixed-effect model. However, the variance in a random-effects model considers both the within-study variance (VYi) and the between-studies variance (T^2).

The inclusion of T^2 in the denominator of the weight formula reflects the random-effects model’s assumption that the true effect size can vary across studies.

This means that in addition to sampling error, there is another source of variability that needs to be accounted for when weighting the studies. The between-studies variance, T^2, represents this additional source of variability.

Here’s the formula for calculating the weight in a random-effects meta-analysis:

W*i = 1 / (VYi + T^2)

• W*i represents the weight assigned to study i.
• T^2 is the estimated between-studies variance.

First, we need to calculate something called τ² (tau squared). This represents the between-study variance.

The estimation of T^2 can be done using different methods, one common approach being the method of moments (DerSimonian and Laird method).

The formula for T^2 using the method of moments is: T^2 = (Q – df) / C

• Q is the homogeneity statistic.
• df is the degrees of freedom (number of studies -1).
• C is a constant calculated based on the study weights
• The weight for each study is then calculated as: Weight = 1 / (within-study variance + τ²). This is different from the fixed effects model because we’re adding τ² to account for between-study variability.

Add up all the weights we calculated in step 1. Divide the sum from step 3 by this total weight

Implications of the random-effects model

• Weights are more balanced between large and small studies compared to the fixed-effects model.
• It’s most appropriate when studies vary in methods, sample characteristics, or other factors that might influence the true effect size.
• The random-effects model typically produces wider confidence intervals, reflecting the additional uncertainty from between-study variability.
• Results are more generalizable to a broader population of studies beyond those included in the meta-analysis.
• This model is often more realistic for social and behavioral sciences, where true effects may vary across different contexts or populations.

Step 10: Sensitivity Analysis

Assess the robustness of your findings by repeating the analysis using different statistical methods, models (fixed-effects and random-effects), or inclusion criteria. This helps determine how sensitive your results are to the choices made during the process.

Sensitivity analysis strengthens a meta-analysis by revealing how robust the findings are to the various decisions and assumptions made during the process. It helps to determine if the conclusions drawn from the meta-analysis hold up when different methods, criteria, or data subsets are used.

This is especially important since opinions may differ on the best approach to conducting a meta-analysis, making the exploration of these variations crucial.

Here are some key ways sensitivity analysis contributes to a more robust meta-analysis:

• Assessing Impact of Different Statistical Methods : A sensitivity analysis can involve calculating the overall effect using different statistical methods, such as fixed and random effects models. This comparison helps determine if the chosen statistical model significantly influences the overall results. For instance, in the meta-analysis of β-blockers after myocardial infarction, both fixed and random effects models yielded almost identical overall estimates. This suggests that the meta-analysis findings are resilient to the statistical method employed.
• Evaluating the Influence of Trial Quality and Size : By analyzing the data with and without trials of questionable quality or varying sizes, researchers can assess the impact of these factors on the overall findings.
• Examining the Effect of Trials Stopped Early : Including trials that were stopped early due to interim analysis results can introduce bias. Sensitivity analysis helps determine if the inclusion or exclusion of such trials noticeably changes the overall effect. In the example of the β-blocker meta-analysis, excluding trials stopped early had a negligible impact on the overall estimate.
• Addressing Publication Bias : It’s essential to assess and account for publication bias, which occurs when studies with statistically significant results are more likely to be published than those with null or nonsignificant findings. This can be accomplished by employing techniques like funnel plots, statistical tests (e.g., Begg and Mazumdar’s rank correlation test, Egger’s test), and sensitivity analyses.

By systematically varying different aspects of the meta-analysis, researchers can assess the robustness of their findings and address potential concerns about the validity of their conclusions.

This process ensures a more reliable and trustworthy synthesis of the research evidence.

Common Mistakes

When conducting a meta-analysis, several common pitfalls can arise, potentially undermining the validity and reliability of the findings. Sources caution against these mistakes and offer guidance on conducting methodologically sound meta-analyses.

• Insufficient Number of Studies: If there are too few primary studies available, a meta-analysis might not be appropriate. While a meta-analysis can technically be conducted with only two studies, the research community might not view findings based on a limited number of studies as reliable evidence. A small number of studies could suggest that the research field is not mature enough for meaningful synthesis.
• Inappropriate Combination of Studies : Meta-analyses should not simply combine studies indiscriminately. Avoid the “apples and oranges” problem, where studies with different research objectives, designs, measures, or samples are inappropriately combined. Such practices can obscure important differences between studies and lead to misleading conclusions.
• Misinterpreting Heterogeneity : One common mistake is using the Q statistic or p-value from a test of heterogeneity as the sole indicator of heterogeneity. While these statistics can signal heterogeneity, they do not quantify the extent of variation in effect sizes.
• Over-Reliance on Published Studies : This dependence on published literature introduces the risk of publication bias, where studies with statistically significant or favorable results are more likely to be published. Failure to acknowledge and address publication bias can lead to overestimating the true effect size.
• Neglecting Study Quality : Including studies with poor methodological quality can bias the results of a meta-analysis leading to unreliable and inaccurate effect size estimates. The decision of which studies to include should be based on predefined eligibility criteria to ensure the quality and relevance of the synthesis.
• Fixation on Statistical Significance : Placing excessive emphasis on the statistical significance of an overall effect while neglecting its practical significance is a critical mistake in meta-analysis, as is the case in primary studies. Considers both statistical and clinical or substantive significance.
• Misinterpreting Significance Testing in Subgroup Analyses : When comparing effect sizes across subgroups, merely observing that an effect is statistically significant in one subgroup but not another is insufficient. Conduct formal tests of statistical significance for the difference in effects between subgroups or to calculate the difference in effects with confidence intervals.
• Ignoring Dependence : Neglecting dependence among effect sizes, particularly when multiple effect sizes are extracted from the same study, is a mistake. This oversight can inflate Type I error rates and lead to inaccurate estimations of average effect sizes and standard errors.
• Inadequate Reporting : Failing to transparently and comprehensively report the meta-analysis process is a crucial mistake. A meta-analysis should include a detailed written protocol outlining the research question, search strategy, inclusion criteria, and analytical methods.

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• Review Article
• Published: 08 March 2018

Meta-analysis and the science of research synthesis

• Jessica Gurevitch 1 ,
• Julia Koricheva 2 ,
• Shinichi Nakagawa 3 , 4 &
• Gavin Stewart 5  

Nature volume  555 ,  pages 175–182 ( 2018 ) Cite this article

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Meta-analysis is the quantitative, scientific synthesis of research results. Since the term and modern approaches to research synthesis were first introduced in the 1970s, meta-analysis has had a revolutionary effect in many scientific fields, helping to establish evidence-based practice and to resolve seemingly contradictory research outcomes. At the same time, its implementation has engendered criticism and controversy, in some cases general and others specific to particular disciplines. Here we take the opportunity provided by the recent fortieth anniversary of meta-analysis to reflect on the accomplishments, limitations, recent advances and directions for future developments in the field of research synthesis.

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Acknowledgements

We dedicate this Review to the memory of Ingram Olkin and William Shadish, founding members of the Society for Research Synthesis Methodology who made tremendous contributions to the development of meta-analysis and research synthesis and to the supervision of generations of students. We thank L. Lagisz for help in preparing the figures. We are grateful to the Center for Open Science and the Laura and John Arnold Foundation for hosting and funding a workshop, which was the origination of this article. S.N. is supported by Australian Research Council Future Fellowship (FT130100268). J.G. acknowledges funding from the US National Science Foundation (ABI 1262402).

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Julia Koricheva

Evolution and Ecology Research Centre and School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, 2052, New South Wales, Australia

Shinichi Nakagawa

Diabetes and Metabolism Division, Garvan Institute of Medical Research, 384 Victoria Street, Darlinghurst, Sydney, 2010, New South Wales, Australia

School of Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK

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Meta-analysis

Reviewed by Psychology Today Staff

Meta-analysis is an objective examination of published data from many studies of the same research topic identified through a literature search. Through the use of rigorous statistical methods, it can reveal patterns hidden in individual studies and can yield conclusions that have a high degree of reliability. It is a method of analysis that is especially useful for gaining an understanding of complex phenomena when independent studies have produced conflicting findings.

Meta-analysis provides much of the underpinning for evidence-based medicine. It is particularly helpful in identifying risk factors for a disorder, diagnostic criteria, and the effects of treatments on specific populations of people, as well as quantifying the size of the effects. Meta-analysis is well-suited to understanding the complexities of human behavior.

• How Does It Differ From Other Studies?
• When Is It Used?
• What Are Some Important Things Revealed by Meta-analysis?

There are well-established scientific criteria for selecting studies for meta-analysis. Usually, meta-analysis is conducted on the gold standard of scientific research—randomized, controlled, double-blind trials. In addition, published guidelines not only describe standards for the inclusion of studies to be analyzed but also rank the quality of different types of studies. For example, cohort studies are likely to provide more reliable information than case reports.

Through statistical methods applied to the original data collected in the included studies, meta-analysis can account for and overcome many differences in the way the studies were conducted, such as the populations studied, how interventions were administered, and what outcomes were assessed and how. Meta-analyses, and the questions they are attempting to answer, are typically specified and registered with a scientific organization, and, with the protocols and methods openly described and reviewed independently by outside investigators, the research process is highly transparent.

Meta-analysis is often used to validate observed phenomena, determine the conditions under which effects occur, and get enough clarity in clinical decision-making to indicate a course of therapeutic action when individual studies have produced disparate findings. In reviewing the aggregate results of well-controlled studies meeting criteria for inclusion, meta-analysis can also reveal which research questions, test conditions, and research methods yield the most reliable results, not only providing findings of immediate clinical utility but furthering science.

The technique can be used to answer social and behavioral questions large and small. For example, to clarify whether or not having more options makes it harder for people to settle on any one item, a meta-analysis of over 53 conflicting studies on the phenomenon was conducted. The meta-analysis revealed that choice overload exists—but only under certain conditions. You will have difficulty selecting a TV show to watch from the massive array of possibilities, for example, if the shows differ from each other in multiple ways or if you don’t have any strong preferences when you finally get to sit down in front of the TV.

A meta-analysis conducted in 2000, for example, answered the question of whether physically attractive people have “better” personalities . Among other traits, they prove to be more extroverted and have more social skills than others. Another meta-analysis, in 2014, showed strong ties between physical attractiveness as rated by others and having good mental and physical health. The effects on such personality factors as extraversion are too small to reliably show up in individual studies but real enough to be detected in the aggregate number of study participants. Together, the studies validate hypotheses put forth by evolutionary psychologists that physical attractiveness is important in mate selection because it is a reliable cue of health and, likely, fertility.

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What is Meta-Analysis? Definition, Research & Examples

Appinio Research · 01.02.2024 · 39min read

Are you looking to harness the power of data and uncover meaningful insights from a multitude of research studies? In a world overflowing with information, meta-analysis emerges as a guiding light, offering a systematic and quantitative approach to distilling knowledge from a sea of research.

This guide will demystify the art and science of meta-analysis, walking you through the process, from defining your research question to interpreting the results. Whether you're an academic researcher, a policymaker, or a curious mind eager to explore the depths of data, this guide will equip you with the tools and understanding needed to undertake robust and impactful meta-analyses.

What is a Meta Analysis?

Meta-analysis is a quantitative research method that involves the systematic synthesis and statistical analysis of data from multiple individual studies on a particular topic or research question. It aims to provide a comprehensive and robust summary of existing evidence by pooling the results of these studies, often leading to more precise and generalizable conclusions.

The primary purpose of meta-analysis is to:

• Quantify Effect Sizes:  Determine the magnitude and direction of an effect or relationship across studies.
• Evaluate Consistency:  Assess the consistency of findings among studies and identify sources of heterogeneity.
• Enhance Statistical Power:  Increase the statistical power to detect significant effects by combining data from multiple studies.
• Generalize Results:  Provide more generalizable results by analyzing a more extensive and diverse sample of participants or contexts.
• Examine Subgroup Effects:  Explore whether the effect varies across different subgroups or study characteristics.

Importance of Meta-Analysis

Meta-analysis plays a crucial role in scientific research and evidence-based decision-making. Here are key reasons why meta-analysis is highly valuable:

• Enhanced Precision:  By pooling data from multiple studies, meta-analysis provides a more precise estimate of the effect size, reducing the impact of random variation.
• Increased Statistical Power:  The combination of numerous studies enhances statistical power, making it easier to detect small but meaningful effects.
• Resolution of Inconsistencies:  Meta-analysis can help resolve conflicting findings in the literature by systematically analyzing and synthesizing evidence.
• Identification of Moderators:  It allows for the identification of factors that may moderate the effect, helping to understand when and for whom interventions or treatments are most effective.
• Evidence-Based Decision-Making:  Policymakers, clinicians, and researchers use meta-analysis to inform evidence-based decision-making, leading to more informed choices in healthcare , education, and other fields.
• Efficient Use of Resources:  Meta-analysis can guide future research by identifying gaps in knowledge, reducing duplication of efforts, and directing resources to areas with the most significant potential impact.

Types of Research Questions Addressed

Meta-analysis can address a wide range of research questions across various disciplines. Some common types of research questions that meta-analysis can tackle include:

• Treatment Efficacy:  Does a specific medical treatment, therapy, or intervention have a significant impact on patient outcomes or symptoms?
• Intervention Effectiveness:  How effective are educational programs, training methods, or interventions in improving learning outcomes or skills?
• Risk Factors and Associations:  What are the associations between specific risk factors, such as smoking or diet, and the likelihood of developing certain diseases or conditions?
• Impact of Policies:  What is the effect of government policies, regulations, or interventions on social, economic, or environmental outcomes?
• Psychological Constructs:  How do psychological constructs, such as self-esteem, anxiety, or motivation, influence behavior or mental health outcomes?
• Comparative Effectiveness:  Which of two or more competing interventions or treatments is more effective for a particular condition or population?
• Dose-Response Relationships:  Is there a dose-response relationship between exposure to a substance or treatment and the likelihood or severity of an outcome?

Meta-analysis is a versatile tool that can provide valuable insights into a wide array of research questions, making it an indispensable method in evidence synthesis and knowledge advancement.

Meta-Analysis vs. Systematic Review

In evidence synthesis and research aggregation, meta-analysis and systematic reviews are two commonly used methods, each serving distinct purposes while sharing some similarities. Let's explore the differences and similarities between these two approaches.

Meta-Analysis

• Purpose:  Meta-analysis is a statistical technique used to combine and analyze quantitative data from multiple individual studies that address the same research question. The primary aim of meta-analysis is to provide a single summary effect size that quantifies the magnitude and direction of an effect or relationship across studies.
• Data Synthesis:  In meta-analysis, researchers extract and analyze numerical data, such as means, standard deviations, correlation coefficients, or odds ratios, from each study. These effect size estimates are then combined using statistical methods to generate an overall effect size and associated confidence interval.
• Quantitative:  Meta-analysis is inherently quantitative, focusing on numerical data and statistical analyses to derive a single effect size estimate.
• Main Outcome:  The main outcome of a meta-analysis is the summary effect size, which provides a quantitative estimate of the research question's answer.

Systematic Review

• Purpose:  A systematic review is a comprehensive and structured overview of the available evidence on a specific research question. While systematic reviews may include meta-analysis, their primary goal is to provide a thorough and unbiased summary of the existing literature.
• Data Synthesis:  Systematic reviews involve a meticulous process of literature search, study selection, data extraction, and quality assessment. Researchers may narratively synthesize the findings, providing a qualitative summary of the evidence.
• Qualitative:  Systematic reviews are often qualitative in nature, summarizing and synthesizing findings in a narrative format. They do not always involve statistical analysis .
• Main Outcome:  The primary outcome of a systematic review is a comprehensive narrative summary of the existing evidence. While some systematic reviews include meta-analyses, not all do so.

Key Differences

• Nature of Data:  Meta-analysis primarily deals with quantitative data and statistical analysis , while systematic reviews encompass both quantitative and qualitative data, often presenting findings in a narrative format.
• Focus on Effect Size:  Meta-analysis focuses on deriving a single, quantitative effect size estimate, whereas systematic reviews emphasize providing a comprehensive overview of the literature, including study characteristics, methodologies, and key findings.
• Synthesis Approach:  Meta-analysis is a quantitative synthesis method, while systematic reviews may use both quantitative and qualitative synthesis approaches.

Commonalities

• Structured Process:  Both meta-analyses and systematic reviews follow a structured and systematic process for literature search, study selection, data extraction, and quality assessment.
• Evidence-Based:  Both approaches aim to provide evidence-based answers to specific research questions, offering valuable insights for decision-making in various fields.
• Transparency:  Both meta-analyses and systematic reviews prioritize transparency and rigor in their methodologies to minimize bias and enhance the reliability of their findings.

While meta-analysis and systematic reviews share the overarching goal of synthesizing research evidence, they differ in their approach and main outcomes. Meta-analysis is quantitative, focusing on effect sizes, while systematic reviews provide comprehensive overviews, utilizing both quantitative and qualitative data to summarize the literature. Depending on the research question and available data, one or both of these methods may be employed to provide valuable insights for evidence-based decision-making.

How to Conduct a Meta-Analysis?

Planning a meta-analysis is a critical phase that lays the groundwork for a successful and meaningful study. We will explore each component of the planning process in more detail, ensuring you have a solid foundation before diving into data analysis.

How to Formulate Research Questions?

Your research questions are the guiding compass of your meta-analysis. They should be precise and tailored to the topic you're investigating. To craft effective research questions:

• Clearly Define the Problem:  Start by identifying the specific problem or topic you want to address through meta-analysis.
• Specify Key Variables:  Determine the essential variables or factors you'll examine in the included studies.
• Frame Hypotheses:  If applicable, create clear hypotheses that your meta-analysis will test.

For example, if you're studying the impact of a specific intervention on patient outcomes, your research question might be: "What is the effect of Intervention X on Patient Outcome Y in published clinical trials?"

Eligibility Criteria

Eligibility criteria define the boundaries of your meta-analysis. By establishing clear criteria, you ensure that the studies you include are relevant and contribute to your research objectives. Key considerations for eligibility criteria include:

• Study Types:  Decide which types of studies will be considered (e.g., randomized controlled trials, cohort studies, case-control studies).
• Publication Time Frame:  Specify the publication date range for included studies.
• Language:  Determine whether studies in languages other than your primary language will be included.
• Geographic Region:  If relevant, define any geographic restrictions.

Your eligibility criteria should strike a balance between inclusivity and relevance. Excluding certain studies based on valid criteria ensures the quality and relevance of the data you analyze.

Search Strategy

A robust search strategy is fundamental to identifying all relevant studies. To create an effective search strategy:

• Select Databases:  Choose appropriate databases that cover your research area (e.g., PubMed, Scopus, Web of Science).
• Keywords and Search Terms:  Develop a comprehensive list of relevant keywords and search terms related to your research questions.
• Search Filters:  Utilize search filters and Boolean operators (AND, OR) to refine your search queries.
• Manual Searches:  Consider conducting hand-searches of key journals and reviewing the reference lists of relevant studies for additional sources.

Remember that the goal is to cast a wide net while maintaining precision to capture all relevant studies.

Data Extraction

Data extraction is the process of systematically collecting information from each selected study. It involves retrieving key data points, including:

• Study Characteristics:  Author(s), publication year, study design, sample size, duration, and location.
• Outcome Data:  Effect sizes, standard errors, confidence intervals, p-values, and any other relevant statistics.
• Methodological Details:  Information on study quality, risk of bias, and potential sources of heterogeneity.

Creating a standardized data extraction form is essential to ensure consistency and accuracy throughout this phase. Spreadsheet software, such as Microsoft Excel, is commonly used for data extraction.

Quality Assessment

Assessing the quality of included studies is crucial to determine their reliability and potential impact on your meta-analysis. Various quality assessment tools and checklists are available, depending on the study design. Some commonly used tools include:

• Newcastle-Ottawa Scale:  Used for assessing the quality of non-randomized studies (e.g., cohort, case-control studies).
• Cochrane Risk of Bias Tool:  Designed for evaluating randomized controlled trials.

Quality assessment typically involves evaluating aspects such as study design, sample size, data collection methods , and potential biases. This step helps you weigh the contribution of each study to the overall analysis.

How to Conduct a Literature Review?

Conducting a thorough literature review is a critical step in the meta-analysis process. We will explore the essential components of a literature review, from designing a comprehensive search strategy to establishing clear inclusion and exclusion criteria and, finally, the study selection process.

Comprehensive Search

To ensure the success of your meta-analysis, it's imperative to cast a wide net when searching for relevant studies. A comprehensive search strategy involves:

• Selecting Relevant Databases:  Identify databases that cover your research area comprehensively, such as PubMed, Scopus, Web of Science, or specialized databases specific to your field.
• Creating a Keyword List:  Develop a list of relevant keywords and search terms related to your research questions. Think broadly and consider synonyms, acronyms, and variations.
• Using Boolean Operators:  Utilize Boolean operators (AND, OR) to combine keywords effectively and refine your search.
• Applying Filters:  Employ search filters (e.g., publication date range, study type) to narrow down results based on your eligibility criteria.

Remember that the goal is to leave no relevant stone unturned, as missing key studies can introduce bias into your meta-analysis.

Inclusion and Exclusion Criteria

Clearly defined inclusion and exclusion criteria are the gatekeepers of your meta-analysis. These criteria ensure that the studies you include meet your research objectives and maintain the quality of your analysis. Consider the following factors when establishing criteria:

• Study Types:  Determine which types of studies are eligible for inclusion (e.g., randomized controlled trials, observational studies, case reports).
• Publication Time Frame:  Specify the time frame within which studies must have been published.
• Language:  Decide whether studies in languages other than your primary language will be included or excluded.
• Geographic Region:  If applicable, define any geographic restrictions.
• Relevance to Research Questions:  Ensure that selected studies align with your research questions and objectives.

Your inclusion and exclusion criteria should strike a balance between inclusivity and relevance. Rigorous criteria help maintain the quality and applicability of the studies included in your meta-analysis.

Study Selection Process

The study selection process involves systematically screening and evaluating each potential study to determine whether it meets your predefined inclusion criteria. Here's a step-by-step guide:

• Screen Titles and Abstracts:  Begin by reviewing the titles and abstracts of the retrieved studies. Exclude studies that clearly do not meet your inclusion criteria.
• Full-Text Assessment:  Assess the full text of potentially relevant studies to confirm their eligibility. Pay attention to study design, sample size, and other specific criteria.
• Data Extraction:  For studies that meet your criteria, extract the necessary data, including study characteristics, effect sizes, and other relevant information.
• Record Exclusions:  Keep a record of the reasons for excluding studies. This transparency is crucial for the reproducibility of your meta-analysis.
• Resolve Discrepancies:  If multiple reviewers are involved, resolve any disagreements through discussion or a third-party arbitrator.

Maintaining a clear and organized record of your study selection process is essential for transparency and reproducibility. Software tools like EndNote or Covidence can facilitate the screening and data extraction process.

By following these systematic steps in conducting a literature review, you ensure that your meta-analysis is built on a solid foundation of relevant and high-quality studies.

Data Extraction and Management

As you progress in your meta-analysis journey, the data extraction and management phase becomes paramount. We will delve deeper into the critical aspects of this phase, including the data collection process, data coding and transformation, and how to handle missing data effectively.

Data Collection Process

The data collection process is the heart of your meta-analysis, where you systematically extract essential information from each selected study. To ensure accuracy and consistency:

• Create a Data Extraction Form:  Develop a standardized data extraction form that includes all the necessary fields for collecting relevant data. This form should align with your research questions and inclusion criteria.
• Data Extractors:  Assign one or more reviewers to extract data from the selected studies. Ensure they are familiar with the form and the specific data points to collect.
• Double-Check Accuracy:  Implement a verification process where a second reviewer cross-checks a random sample of data extractions to identify discrepancies or errors.
• Extract All Relevant Information:  Collect data on study characteristics, participant demographics, outcome measures, effect sizes, confidence intervals, and any additional information required for your analysis.
• Maintain Consistency:  Use clear guidelines and definitions for data extraction to ensure uniformity across studies.

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Data Coding and Transformation

After data collection, you may need to code and transform the extracted data to ensure uniformity and compatibility across studies. This process involves:

• Coding Categorical Variables:  If studies report data differently, code categorical variables consistently . For example, ensure that categories like "male" and "female" are coded consistently across studies.
• Standardizing Units of Measurement:  Convert all measurements to a common unit if studies use different measurement units. For instance, if one study reports height in inches and another in centimeters, standardize to one unit for comparability.
• Calculating Effect Sizes:  Calculate effect sizes and their standard errors or variances if they are not directly reported in the studies. Common effect size measures include Cohen's d, odds ratio (OR), and hazard ratio (HR).
• Data Transformation:  Transform data if necessary to meet assumptions of statistical tests. Common transformations include log transformation for skewed data or arcsine transformation for proportions.
• Heterogeneity Adjustment:  Consider using transformation methods to address heterogeneity among studies, such as applying the Freeman-Tukey double arcsine transformation for proportions.

The goal of data coding and transformation is to make sure that data from different studies are compatible and can be effectively synthesized during the analysis phase. Spreadsheet software like Excel or statistical software like R can be used for these tasks.

Handling Missing Data

Missing data is a common challenge in meta-analysis, and how you handle it can impact the validity and precision of your results. Strategies for handling missing data include:

• Contact Authors:  If feasible, contact the authors of the original studies to request missing data or clarifications.
• Imputation:  Consider using appropriate imputation methods to estimate missing values, but exercise caution and report the imputation methods used.
• Sensitivity Analysis:  Conduct sensitivity analyses to assess the impact of missing data on your results by comparing the main analysis to alternative scenarios.

Remember that transparency in reporting how you handled missing data is crucial for the credibility of your meta-analysis.

By following these steps in data extraction and management, you will ensure the integrity and reliability of your meta-analysis dataset.

Meta-Analysis Example

Meta-analysis is a versatile research method that can be applied to various fields and disciplines, providing valuable insights by synthesizing existing evidence.

Example 1: Analyzing the Impact of Advertising Campaigns on Sales

Background:  A market research agency is tasked with assessing the effectiveness of advertising campaigns on sales outcomes for a range of consumer products. They have access to multiple studies and reports conducted by different companies, each analyzing the impact of advertising on sales revenue.

Meta-Analysis Approach:

• Study Selection:  Identify relevant studies that meet specific inclusion criteria, such as the type of advertising campaign (e.g., TV commercials, social media ads), the products examined, and the sales metrics assessed.
• Data Extraction:  Collect data from each study, including details about the advertising campaign (e.g., budget, duration), sales data (e.g., revenue, units sold), and any reported effect sizes or correlations.
• Effect Size Calculation:  Calculate effect sizes (e.g., correlation coefficients) based on the data provided in each study, quantifying the strength and direction of the relationship between advertising and sales.
• Data Synthesis:  Employ meta-analysis techniques to combine the effect sizes from the selected studies. Compute a summary effect size and its confidence interval to estimate the overall impact of advertising on sales.
• Publication Bias Assessment:  Use funnel plots and statistical tests to assess the potential presence of publication bias, ensuring that the meta-analysis results are not unduly influenced by selective reporting.

Findings:  Through meta-analysis, the market research agency discovers that advertising campaigns have a statistically significant and positive impact on sales across various product categories. The findings provide evidence for the effectiveness of advertising efforts and assist companies in making data-driven decisions regarding their marketing strategies.

These examples illustrate how meta-analysis can be applied in diverse domains, from tech startups seeking to optimize user engagement to market research agencies evaluating the impact of advertising campaigns. By systematically synthesizing existing evidence, meta-analysis empowers decision-makers with valuable insights for informed choices and evidence-based strategies.

How to Assess Study Quality and Bias?

Ensuring the quality and reliability of the studies included in your meta-analysis is essential for drawing accurate conclusions. We'll show you how you can assess study quality using specific tools, evaluate potential bias, and address publication bias.

Quality Assessment Tools

Quality assessment tools provide structured frameworks for evaluating the methodological rigor of each included study. The choice of tool depends on the study design. Here are some commonly used quality assessment tools:

For Randomized Controlled Trials (RCTs):

• Cochrane Risk of Bias Tool:  This tool assesses the risk of bias in RCTs based on six domains: random sequence generation, allocation concealment, blinding of participants and personnel, blinding of outcome assessment, incomplete outcome data, and selective reporting.
• Jadad Scale:  A simpler tool specifically for RCTs, the Jadad Scale focuses on randomization, blinding, and the handling of withdrawals and dropouts.

For Observational Studies:

• Newcastle-Ottawa Scale (NOS):  The NOS assesses the quality of cohort and case-control studies based on three categories: selection, comparability, and outcome.
• ROBINS-I:  Designed for non-randomized studies of interventions, the Risk of Bias in Non-randomized Studies of Interventions tool evaluates bias in domains such as confounding, selection bias, and measurement bias.
• MINORS:  The Methodological Index for Non-Randomized Studies (MINORS) assesses non-comparative studies and includes items related to study design, reporting, and statistical analysis.

Bias Assessment

Evaluating potential sources of bias is crucial to understanding the limitations of the included studies. Common sources of bias include:

• Selection Bias:  Occurs when the selection of participants is not random or representative of the target population.
• Performance Bias:  Arises when participants or researchers are aware of the treatment or intervention status, potentially influencing outcomes.
• Detection Bias:  Occurs when outcome assessors are not blinded to the treatment groups.
• Attrition Bias:  Results from incomplete data or differential loss to follow-up between treatment groups.
• Reporting Bias:  Involves selective reporting of outcomes, where only positive or statistically significant results are published.

To assess bias, reviewers often use the quality assessment tools mentioned earlier, which include domains related to bias, or they may specifically address bias concerns in the narrative synthesis.

We'll move on to the core of meta-analysis: data synthesis. We'll explore different effect size measures, fixed-effect versus random-effects models, and techniques for assessing and addressing heterogeneity among studies.

Data Synthesis

Now that you've gathered data from multiple studies and assessed their quality, it's time to synthesize this information effectively.

Effect Size Measures

Effect size measures quantify the magnitude of the relationship or difference you're investigating in your meta-analysis. The choice of effect size measure depends on your research question and the type of data provided by the included studies. Here are some commonly used effect size measures:

Continuous Outcome Data:

• Cohen's d:  Measures the standardized mean difference between two groups. It's suitable for continuous outcome variables.
• Hedges' g:  Similar to Cohen's d but incorporates a correction factor for small sample sizes.

Binary Outcome Data:

• Odds Ratio (OR):  Used for dichotomous outcomes, such as success/failure or presence/absence.
• Risk Ratio (RR):  Similar to OR but used when the outcome is relatively common.

Time-to-Event Data:

• Hazard Ratio (HR):  Used in survival analysis to assess the risk of an event occurring over time.
• Risk Difference (RD):  Measures the absolute difference in event rates between two groups.

Selecting the appropriate effect size measure depends on the nature of your data and the research question. When effect sizes are not directly reported in the studies, you may need to calculate them using available data, such as means, standard deviations, and sample sizes.

Formula for Cohen's d:

d = (Mean of Group A - Mean of Group B) / Pooled Standard Deviation

Fixed-Effect vs. Random-Effects Models

In meta-analysis, you can choose between fixed-effect and random-effects models to combine the results of individual studies:

Fixed-Effect Model:

• Assumes that all included studies share a common true effect size.
• Accounts for only within-study variability ( sampling error ).
• Appropriate when studies are very similar or when there's minimal heterogeneity.

Random-Effects Model:

• Acknowledges that there may be variability in effect sizes across studies.
• Accounts for both within-study variability (sampling error) and between-study variability (real differences between studies).
• More conservative and applicable when there's substantial heterogeneity.

The choice between these models should be guided by the degree of heterogeneity observed among the included studies. If heterogeneity is significant, the random-effects model is often preferred, as it provides a more robust estimate of the overall effect.

Forest Plots

Forest plots are graphical representations commonly used in meta-analysis to display the results of individual studies along with the combined summary estimate. Key components of a forest plot include:

• Vertical Line:  Represents the null effect (e.g., no difference or no effect).
• Horizontal Lines:  Represent the confidence intervals for each study's effect size estimate.
• Diamond or Square:  Represents the summary effect size estimate, with its width indicating the confidence interval around the summary estimate.
• Study Names:  Listed on the left side of the plot, identifying each study.

Forest plots help visualize the distribution of effect sizes across studies and provide insights into the consistency and direction of the findings.

Heterogeneity Assessment

Heterogeneity refers to the variability in effect sizes among the included studies. It's important to assess and understand heterogeneity as it can impact the interpretation of your meta-analysis results. Standard methods for assessing heterogeneity include:

• Cochran's Q Test:  A statistical test that assesses whether there is significant heterogeneity among the effect sizes of the included studies.
• I² Statistic:  A measure that quantifies the proportion of total variation in effect sizes that is due to heterogeneity. I² values range from 0% to 100%, with higher values indicating greater heterogeneity.

Assessing heterogeneity is crucial because it informs your choice of meta-analysis model (fixed-effect vs. random-effects) and whether subgroup analyses or sensitivity analyses are warranted to explore potential sources of heterogeneity.

How to Interpret Meta-Analysis Results?

With the data synthesis complete, it's time to make sense of the results of your meta-analysis.

Meta-Analytic Summary

The meta-analytic summary is the culmination of your efforts in data synthesis. It provides a consolidated estimate of the effect size and its confidence interval, combining the results of all included studies. To interpret the meta-analytic summary effectively:

• Effect Size Estimate:  Understand the primary effect size estimate, such as Cohen's d, odds ratio, or hazard ratio, and its associated confidence interval.
• Significance:  Determine whether the summary effect size is statistically significant. This is indicated when the confidence interval does not include the null value (e.g., 0 for Cohen's d or 1 for odds ratio).
• Magnitude:  Assess the magnitude of the effect size. Is it large, moderate, or small, and what are the practical implications of this magnitude?
• Direction:  Consider the direction of the effect. Is it in the hypothesized direction, or does it contradict the expected outcome?
• Clinical or Practical Significance:  Reflect on the clinical or practical significance of the findings. Does the effect size have real-world implications?
• Consistency:  Evaluate the consistency of the findings across studies. Are most studies in agreement with the summary effect size estimate, or are there outliers?

Subgroup Analyses

Subgroup analyses allow you to explore whether the effect size varies across different subgroups of studies or participants. This can help identify potential sources of heterogeneity or assess whether the intervention's effect differs based on specific characteristics. Steps for conducting subgroup analyses:

• Define Subgroups:  Clearly define the subgroups you want to investigate based on relevant study characteristics (e.g., age groups, study design , intervention type).
• Analyze Subgroups:  Calculate separate summary effect sizes for each subgroup and compare them to the overall summary effect.
• Assess Heterogeneity:  Evaluate whether subgroup differences are statistically significant. If so, this suggests that the effect size varies significantly among subgroups.
• Interpretation:  Interpret the subgroup findings in the context of your research question. Are there meaningful differences in the effect across subgroups? What might explain these differences?

Subgroup analyses can provide valuable insights into the factors influencing the overall effect size and help tailor recommendations for specific populations or conditions.

Sensitivity Analyses

Sensitivity analyses are conducted to assess the robustness of your meta-analysis results by exploring how different choices or assumptions might affect the findings. Common sensitivity analyses include:

• Exclusion of Low-Quality Studies:  Repeating the meta-analysis after excluding studies with low quality or a high risk of bias.
• Changing Effect Size Measure:  Re-running the analysis using a different effect size measure to assess whether the choice of measure significantly impacts the results.
• Publication Bias Adjustment:  Applying methods like the trim-and-fill procedure to adjust for potential publication bias.
• Subsample Analysis:  Analyzing a subset of studies based on specific criteria or characteristics to investigate their impact on the summary effect.

Sensitivity analyses help assess the robustness and reliability of your meta-analysis results, providing a more comprehensive understanding of the potential influence of various factors.

Reporting and Publication

The final stages of your meta-analysis involve preparing your findings for publication.

Manuscript Preparation

When preparing your meta-analysis manuscript, consider the following:

• Structured Format:  Organize your manuscript following a structured format, including sections such as introduction, methods, results, discussion, and conclusions.
• Clarity and Conciseness:  Write your findings clearly and concisely, avoiding jargon or overly technical language. Use tables and figures to enhance clarity.
• Transparent Methods:  Provide detailed descriptions of your methods, including eligibility criteria, search strategy, data extraction, and statistical analysis.
• Incorporate Tables and Figures:  Present your meta-analysis results using tables and forest plots to visually convey key findings.
• Interpretation:  Interpret the implications of your findings, discussing the clinical or practical significance and limitations.

Transparent Reporting Guidelines

Adhering to transparent reporting guidelines ensures that your meta-analysis is transparent, reproducible, and credible. Some widely recognized guidelines include:

• PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses):  PRISMA provides a checklist and flow diagram for reporting systematic reviews and meta-analyses, enhancing transparency and rigor.
• MOOSE (Meta-analysis of Observational Studies in Epidemiology):  MOOSE guidelines are designed for meta-analyses of observational studies and provide a framework for transparent reporting.
• ROBINS-I:  If your meta-analysis involves non-randomized studies, follow the Risk Of Bias In Non-randomized Studies of Interventions guidelines for reporting.

Adhering to these guidelines ensures that your meta-analysis is transparent, reproducible, and credible. It enhances the quality of your research and aids readers and reviewers in assessing the rigor of your study.

PRISMA Statement

The PRISMA statement is a valuable resource for conducting and reporting systematic reviews and meta-analyses. Key elements of PRISMA include:

• Title:  Clearly indicate that your paper is a systematic review or meta-analysis.
• Structured Abstract:  Provide a structured summary of your study, including objectives, methods, results, and conclusions.
• Transparent Reporting:  Follow the PRISMA checklist, which covers items such as the rationale, eligibility criteria, search strategy, data extraction, and risk of bias assessment.
• Flow Diagram:  Include a flow diagram illustrating the study selection process.

By adhering to the PRISMA statement, you enhance the transparency and credibility of your meta-analysis, facilitating its acceptance for publication and aiding readers in evaluating the quality of your research.

Conclusion for Meta-Analysis

Meta-analysis is a powerful tool that allows you to combine and analyze data from multiple studies to find meaningful patterns and make informed decisions. It helps you see the bigger picture and draw more accurate conclusions than individual studies alone. Whether you're in healthcare, education, business, or any other field, the principles of meta-analysis can be applied to enhance your research and decision-making processes. Remember that conducting a successful meta-analysis requires careful planning, attention to detail, and transparency in reporting. By following the steps outlined in this guide, you can embark on your own meta-analysis journey with confidence, contributing to the advancement of knowledge and evidence-based practices in your area of interest.

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Practical Guide to Meta-analysis

• 1 Stanford-Surgery Policy Improvement, Research and Education (S-SPIRE) Center, Palo Alto, California
• 2 Department of Biostatistics, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill
• 3 Department of Surgery, University of Michigan, Ann Arbor
• Editorial Maximizing the Impact of Surgical Health Services Research Amir A. Ghaferi, MD, MS; Adil H. Haider, MD, MPH; Melina R. Kibbe, MD JAMA Surgery
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• Guide to Statistics and Methods Practical Guide to Mixed Methods Lesly A. Dossett, MD, MPH; Amy H. Kaji, MD, PhD; Justin B. Dimick, MD, MPH JAMA Surgery
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• Guide to Statistics and Methods Practical Guide to Survey Research Karen Brasel, MD, MPH; Adil Haider, MD, MPH; Jason Haukoos, MD, MSc JAMA Surgery
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• Guide to Statistics and Methods Practical Guide to Implementation Science Heather B. Neuman, MD, MS; Amy H. Kaji, MD, PhD; Elliott R. Haut, MD, PhD JAMA Surgery
• Guide to Statistics and Methods Practical Guide to Decision Analysis Dorry L. Segev, MD, PhD; Jason S. Haukoos, MD, MSc; Timothy M. Pawlik, MD, MPH, PhD JAMA Surgery

Meta-analysis is a systematic approach of synthesizing, combining, and analyzing data from multiple studies (randomized clinical trials 1 or observational studies 2 ) into a single effect estimate to answer a research question. Meta-analysis is especially useful if there is debate around the research question in the literature published to date or the individual published studies are underpowered. Vital to a high-quality meta-analysis is a comprehensive literature search, prespecified hypothesis and aims, reporting of study quality, consideration of heterogeneity and examination of bias. In the hierarchy of evidence, meta-analysis appears above observational studies and randomized clinical trials because it rigorously collates evidence across a larger body of literature; however, meta-analysis is largely dependent on the quality of the primary data.

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Cochrane Training

Chapter 10: analysing data and undertaking meta-analyses.

Jonathan J Deeks, Julian PT Higgins, Douglas G Altman; on behalf of the Cochrane Statistical Methods Group

Key Points:

• Meta-analysis is the statistical combination of results from two or more separate studies.
• Potential advantages of meta-analyses include an improvement in precision, the ability to answer questions not posed by individual studies, and the opportunity to settle controversies arising from conflicting claims. However, they also have the potential to mislead seriously, particularly if specific study designs, within-study biases, variation across studies, and reporting biases are not carefully considered.
• It is important to be familiar with the type of data (e.g. dichotomous, continuous) that result from measurement of an outcome in an individual study, and to choose suitable effect measures for comparing intervention groups.
• Most meta-analysis methods are variations on a weighted average of the effect estimates from the different studies.
• Studies with no events contribute no information about the risk ratio or odds ratio. For rare events, the Peto method has been observed to be less biased and more powerful than other methods.
• Variation across studies (heterogeneity) must be considered, although most Cochrane Reviews do not have enough studies to allow for the reliable investigation of its causes. Random-effects meta-analyses allow for heterogeneity by assuming that underlying effects follow a normal distribution, but they must be interpreted carefully. Prediction intervals from random-effects meta-analyses are a useful device for presenting the extent of between-study variation.
• Many judgements are required in the process of preparing a meta-analysis. Sensitivity analyses should be used to examine whether overall findings are robust to potentially influential decisions.

Cite this chapter as: Deeks JJ, Higgins JPT, Altman DG (editors). Chapter 10: Analysing data and undertaking meta-analyses. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.4 (updated August  2023). Cochrane, 2023. Available from www.training.cochrane.org/handbook .

10.1 Do not start here!

It can be tempting to jump prematurely into a statistical analysis when undertaking a systematic review. The production of a diamond at the bottom of a plot is an exciting moment for many authors, but results of meta-analyses can be very misleading if suitable attention has not been given to formulating the review question; specifying eligibility criteria; identifying and selecting studies; collecting appropriate data; considering risk of bias; planning intervention comparisons; and deciding what data would be meaningful to analyse. Review authors should consult the chapters that precede this one before a meta-analysis is undertaken.

10.2 Introduction to meta-analysis

An important step in a systematic review is the thoughtful consideration of whether it is appropriate to combine the numerical results of all, or perhaps some, of the studies. Such a meta-analysis yields an overall statistic (together with its confidence interval) that summarizes the effectiveness of an experimental intervention compared with a comparator intervention. Potential advantages of meta-analyses include the following:

• T o improve precision . Many studies are too small to provide convincing evidence about intervention effects in isolation. Estimation is usually improved when it is based on more information.
• To answer questions not posed by the individual studies . Primary studies often involve a specific type of participant and explicitly defined interventions. A selection of studies in which these characteristics differ can allow investigation of the consistency of effect across a wider range of populations and interventions. It may also, if relevant, allow reasons for differences in effect estimates to be investigated.
• To settle controversies arising from apparently conflicting studies or to generate new hypotheses . Statistical synthesis of findings allows the degree of conflict to be formally assessed, and reasons for different results to be explored and quantified.

Of course, the use of statistical synthesis methods does not guarantee that the results of a review are valid, any more than it does for a primary study. Moreover, like any tool, statistical methods can be misused.

This chapter describes the principles and methods used to carry out a meta-analysis for a comparison of two interventions for the main types of data encountered. The use of network meta-analysis to compare more than two interventions is addressed in Chapter 11 . Formulae for most of the methods described are provided in the RevMan Web Knowledge Base under Statistical Algorithms and calculations used in Review Manager (documentation.cochrane.org/revman-kb/statistical-methods-210600101.html), and a longer discussion of many of the issues is available ( Deeks et al 2001 ).

10.2.1 Principles of meta-analysis

The commonly used methods for meta-analysis follow the following basic principles:

• Meta-analysis is typically a two-stage process. In the first stage, a summary statistic is calculated for each study, to describe the observed intervention effect in the same way for every study. For example, the summary statistic may be a risk ratio if the data are dichotomous, or a difference between means if the data are continuous (see Chapter 6 ).

• The combination of intervention effect estimates across studies may optionally incorporate an assumption that the studies are not all estimating the same intervention effect, but estimate intervention effects that follow a distribution across studies. This is the basis of a random-effects meta-analysis (see Section 10.10.4 ). Alternatively, if it is assumed that each study is estimating exactly the same quantity, then a fixed-effect meta-analysis is performed.
• The standard error of the summary intervention effect can be used to derive a confidence interval, which communicates the precision (or uncertainty) of the summary estimate; and to derive a P value, which communicates the strength of the evidence against the null hypothesis of no intervention effect.
• As well as yielding a summary quantification of the intervention effect, all methods of meta-analysis can incorporate an assessment of whether the variation among the results of the separate studies is compatible with random variation, or whether it is large enough to indicate inconsistency of intervention effects across studies (see Section 10.10 ).
• The problem of missing data is one of the numerous practical considerations that must be thought through when undertaking a meta-analysis. In particular, review authors should consider the implications of missing outcome data from individual participants (due to losses to follow-up or exclusions from analysis) (see Section 10.12 ).

Meta-analyses are usually illustrated using a forest plot . An example appears in Figure 10.2.a . A forest plot displays effect estimates and confidence intervals for both individual studies and meta-analyses (Lewis and Clarke 2001). Each study is represented by a block at the point estimate of intervention effect with a horizontal line extending either side of the block. The area of the block indicates the weight assigned to that study in the meta-analysis while the horizontal line depicts the confidence interval (usually with a 95% level of confidence). The area of the block and the confidence interval convey similar information, but both make different contributions to the graphic. The confidence interval depicts the range of intervention effects compatible with the study’s result. The size of the block draws the eye towards the studies with larger weight (usually those with narrower confidence intervals), which dominate the calculation of the summary result, presented as a diamond at the bottom.

Figure 10.2.a Example of a forest plot from a review of interventions to promote ownership of smoke alarms (DiGuiseppi and Higgins 2001). Reproduced with permission of John Wiley & Sons

10.3 A generic inverse-variance approach to meta-analysis

A very common and simple version of the meta-analysis procedure is commonly referred to as the inverse-variance method . This approach is implemented in its most basic form in RevMan, and is used behind the scenes in many meta-analyses of both dichotomous and continuous data.

The inverse-variance method is so named because the weight given to each study is chosen to be the inverse of the variance of the effect estimate (i.e. 1 over the square of its standard error). Thus, larger studies, which have smaller standard errors, are given more weight than smaller studies, which have larger standard errors. This choice of weights minimizes the imprecision (uncertainty) of the pooled effect estimate.

10.3.1 Fixed-effect method for meta-analysis

A fixed-effect meta-analysis using the inverse-variance method calculates a weighted average as:

where Y i is the intervention effect estimated in the i th study, SE i is the standard error of that estimate, and the summation is across all studies. The basic data required for the analysis are therefore an estimate of the intervention effect and its standard error from each study. A fixed-effect meta-analysis is valid under an assumption that all effect estimates are estimating the same underlying intervention effect, which is referred to variously as a ‘fixed-effect’ assumption, a ‘common-effect’ assumption or an ‘equal-effects’ assumption. However, the result of the meta-analysis can be interpreted without making such an assumption (Rice et al 2018).

10.3.2 Random-effects methods for meta-analysis

A variation on the inverse-variance method is to incorporate an assumption that the different studies are estimating different, yet related, intervention effects (Higgins et al 2009). This produces a random-effects meta-analysis, and the simplest version is known as the DerSimonian and Laird method (DerSimonian and Laird 1986). Random-effects meta-analysis is discussed in detail in Section 10.10.4 .

10.3.3 Performing inverse-variance meta-analyses

Most meta-analysis programs perform inverse-variance meta-analyses. Usually the user provides summary data from each intervention arm of each study, such as a 2×2 table when the outcome is dichotomous (see Chapter 6, Section 6.4 ), or means, standard deviations and sample sizes for each group when the outcome is continuous (see Chapter 6, Section 6.5 ). This avoids the need for the author to calculate effect estimates, and allows the use of methods targeted specifically at different types of data (see Sections 10.4 and 10.5 ).

When the data are conveniently available as summary statistics from each intervention group, the inverse-variance method can be implemented directly. For example, estimates and their standard errors may be entered directly into RevMan under the ‘Generic inverse variance’ outcome type. For ratio measures of intervention effect, the data must be entered into RevMan as natural logarithms (for example, as a log odds ratio and the standard error of the log odds ratio). However, it is straightforward to instruct the software to display results on the original (e.g. odds ratio) scale. It is possible to supplement or replace this with a column providing the sample sizes in the two groups. Note that the ability to enter estimates and standard errors creates a high degree of flexibility in meta-analysis. It facilitates the analysis of properly analysed crossover trials, cluster-randomized trials and non-randomized trials (see Chapter 23 ), as well as outcome data that are ordinal, time-to-event or rates (see Chapter 6 ).

10.4 Meta-analysis of dichotomous outcomes

There are four widely used methods of meta-analysis for dichotomous outcomes, three fixed-effect methods (Mantel-Haenszel, Peto and inverse variance) and one random-effects method (DerSimonian and Laird inverse variance). All of these methods are available as analysis options in RevMan. The Peto method can only combine odds ratios, whilst the other three methods can combine odds ratios, risk ratios or risk differences. Formulae for all of the meta-analysis methods are available elsewhere (Deeks et al 2001).

Note that having no events in one group (sometimes referred to as ‘zero cells’) causes problems with computation of estimates and standard errors with some methods: see Section 10.4.4 .

10.4.1 Mantel-Haenszel methods

When data are sparse, either in terms of event risks being low or study size being small, the estimates of the standard errors of the effect estimates that are used in the inverse-variance methods may be poor. Mantel-Haenszel methods are fixed-effect meta-analysis methods using a different weighting scheme that depends on which effect measure (e.g. risk ratio, odds ratio, risk difference) is being used (Mantel and Haenszel 1959, Greenland and Robins 1985). They have been shown to have better statistical properties when there are few events. As this is a common situation in Cochrane Reviews, the Mantel-Haenszel method is generally preferable to the inverse variance method in fixed-effect meta-analyses. In other situations the two methods give similar estimates.

10.4.2 Peto odds ratio method

Peto’s method can only be used to combine odds ratios (Yusuf et al 1985). It uses an inverse-variance approach, but uses an approximate method of estimating the log odds ratio, and uses different weights. An alternative way of viewing the Peto method is as a sum of ‘O – E’ statistics. Here, O is the observed number of events and E is an expected number of events in the experimental intervention group of each study under the null hypothesis of no intervention effect.

The approximation used in the computation of the log odds ratio works well when intervention effects are small (odds ratios are close to 1), events are not particularly common and the studies have similar numbers in experimental and comparator groups. In other situations it has been shown to give biased answers. As these criteria are not always fulfilled, Peto’s method is not recommended as a default approach for meta-analysis.

Corrections for zero cell counts are not necessary when using Peto’s method. Perhaps for this reason, this method performs well when events are very rare (Bradburn et al 2007); see Section 10.4.4.1 . Also, Peto’s method can be used to combine studies with dichotomous outcome data with studies using time-to-event analyses where log-rank tests have been used (see Section 10.9 ).

10.4.3 Which effect measure for dichotomous outcomes?

Effect measures for dichotomous data are described in Chapter 6, Section 6.4.1 . The effect of an intervention can be expressed as either a relative or an absolute effect. The risk ratio (relative risk) and odds ratio are relative measures, while the risk difference and number needed to treat for an additional beneficial outcome are absolute measures. A further complication is that there are, in fact, two risk ratios. We can calculate the risk ratio of an event occurring or the risk ratio of no event occurring. These give different summary results in a meta-analysis, sometimes dramatically so.

The selection of a summary statistic for use in meta-analysis depends on balancing three criteria (Deeks 2002). First, we desire a summary statistic that gives values that are similar for all the studies in the meta-analysis and subdivisions of the population to which the interventions will be applied. The more consistent the summary statistic, the greater is the justification for expressing the intervention effect as a single summary number. Second, the summary statistic must have the mathematical properties required to perform a valid meta-analysis. Third, the summary statistic would ideally be easily understood and applied by those using the review. The summary intervention effect should be presented in a way that helps readers to interpret and apply the results appropriately. Among effect measures for dichotomous data, no single measure is uniformly best, so the choice inevitably involves a compromise.

Consistency Empirical evidence suggests that relative effect measures are, on average, more consistent than absolute measures (Engels et al 2000, Deeks 2002, Rücker et al 2009). For this reason, it is wise to avoid performing meta-analyses of risk differences, unless there is a clear reason to suspect that risk differences will be consistent in a particular clinical situation. On average there is little difference between the odds ratio and risk ratio in terms of consistency (Deeks 2002). When the study aims to reduce the incidence of an adverse event, there is empirical evidence that risk ratios of the adverse event are more consistent than risk ratios of the non-event (Deeks 2002). Selecting an effect measure based on what is the most consistent in a particular situation is not a generally recommended strategy, since it may lead to a selection that spuriously maximizes the precision of a meta-analysis estimate.

Mathematical properties The most important mathematical criterion is the availability of a reliable variance estimate. The number needed to treat for an additional beneficial outcome does not have a simple variance estimator and cannot easily be used directly in meta-analysis, although it can be computed from the meta-analysis result afterwards (see Chapter 15, Section 15.4.2 ). There is no consensus regarding the importance of two other often-cited mathematical properties: the fact that the behaviour of the odds ratio and the risk difference do not rely on which of the two outcome states is coded as the event, and the odds ratio being the only statistic which is unbounded (see Chapter 6, Section 6.4.1 ).

Ease of interpretation The odds ratio is the hardest summary statistic to understand and to apply in practice, and many practising clinicians report difficulties in using them. There are many published examples where authors have misinterpreted odds ratios from meta-analyses as risk ratios. Although odds ratios can be re-expressed for interpretation (as discussed here), there must be some concern that routine presentation of the results of systematic reviews as odds ratios will lead to frequent over-estimation of the benefits and harms of interventions when the results are applied in clinical practice. Absolute measures of effect are thought to be more easily interpreted by clinicians than relative effects (Sinclair and Bracken 1994), and allow trade-offs to be made between likely benefits and likely harms of interventions. However, they are less likely to be generalizable.

It is generally recommended that meta-analyses are undertaken using risk ratios (taking care to make a sensible choice over which category of outcome is classified as the event) or odds ratios. This is because it seems important to avoid using summary statistics for which there is empirical evidence that they are unlikely to give consistent estimates of intervention effects (the risk difference), and it is impossible to use statistics for which meta-analysis cannot be performed (the number needed to treat for an additional beneficial outcome). It may be wise to plan to undertake a sensitivity analysis to investigate whether choice of summary statistic (and selection of the event category) is critical to the conclusions of the meta-analysis (see Section 10.14 ).

It is often sensible to use one statistic for meta-analysis and to re-express the results using a second, more easily interpretable statistic. For example, often meta-analysis may be best performed using relative effect measures (risk ratios or odds ratios) and the results re-expressed using absolute effect measures (risk differences or numbers needed to treat for an additional beneficial outcome – see Chapter 15, Section 15.4 . This is one of the key motivations for ‘Summary of findings’ tables in Cochrane Reviews: see Chapter 14 ). If odds ratios are used for meta-analysis they can also be re-expressed as risk ratios (see Chapter 15, Section 15.4 ). In all cases the same formulae can be used to convert upper and lower confidence limits. However, all of these transformations require specification of a value of baseline risk that indicates the likely risk of the outcome in the ‘control’ population to which the experimental intervention will be applied. Where the chosen value for this assumed comparator group risk is close to the typical observed comparator group risks across the studies, similar estimates of absolute effect will be obtained regardless of whether odds ratios or risk ratios are used for meta-analysis. Where the assumed comparator risk differs from the typical observed comparator group risk, the predictions of absolute benefit will differ according to which summary statistic was used for meta-analysis.

10.4.4 Meta-analysis of rare events

For rare outcomes, meta-analysis may be the only way to obtain reliable evidence of the effects of healthcare interventions. Individual studies are usually under-powered to detect differences in rare outcomes, but a meta-analysis of many studies may have adequate power to investigate whether interventions do have an impact on the incidence of the rare event. However, many methods of meta-analysis are based on large sample approximations, and are unsuitable when events are rare. Thus authors must take care when selecting a method of meta-analysis (Efthimiou 2018).

There is no single risk at which events are classified as ‘rare’. Certainly risks of 1 in 1000 constitute rare events, and many would classify risks of 1 in 100 the same way. However, the performance of methods when risks are as high as 1 in 10 may also be affected by the issues discussed in this section. What is typical is that a high proportion of the studies in the meta-analysis observe no events in one or more study arms.

10.4.4.1 Studies with no events in one or more arms

Computational problems can occur when no events are observed in one or both groups in an individual study. Inverse variance meta-analytical methods involve computing an intervention effect estimate and its standard error for each study. For studies where no events were observed in one or both arms, these computations often involve dividing by a zero count, which yields a computational error. Most meta-analytical software routines (including those in RevMan) automatically check for problematic zero counts, and add a fixed value (typically 0.5) to all cells of a 2×2 table where the problems occur. The Mantel-Haenszel methods require zero-cell corrections only if the same cell is zero in all the included studies, and hence need to use the correction less often. However, in many software applications the same correction rules are applied for Mantel-Haenszel methods as for the inverse-variance methods. Odds ratio and risk ratio methods require zero cell corrections more often than difference methods, except for the Peto odds ratio method, which encounters computation problems only in the extreme situation of no events occurring in all arms of all studies.

Whilst the fixed correction meets the objective of avoiding computational errors, it usually has the undesirable effect of biasing study estimates towards no difference and over-estimating variances of study estimates (consequently down-weighting inappropriately their contribution to the meta-analysis). Where the sizes of the study arms are unequal (which occurs more commonly in non-randomized studies than randomized trials), they will introduce a directional bias in the treatment effect. Alternative non-fixed zero-cell corrections have been explored by Sweeting and colleagues, including a correction proportional to the reciprocal of the size of the contrasting study arm, which they found preferable to the fixed 0.5 correction when arm sizes were not balanced (Sweeting et al 2004).

10.4.4.2 Studies with no events in either arm

The standard practice in meta-analysis of odds ratios and risk ratios is to exclude studies from the meta-analysis where there are no events in both arms. This is because such studies do not provide any indication of either the direction or magnitude of the relative treatment effect. Whilst it may be clear that events are very rare on both the experimental intervention and the comparator intervention, no information is provided as to which group is likely to have the higher risk, or on whether the risks are of the same or different orders of magnitude (when risks are very low, they are compatible with very large or very small ratios). Whilst one might be tempted to infer that the risk would be lowest in the group with the larger sample size (as the upper limit of the confidence interval would be lower), this is not justified as the sample size allocation was determined by the study investigators and is not a measure of the incidence of the event.

Risk difference methods superficially appear to have an advantage over odds ratio methods in that the risk difference is defined (as zero) when no events occur in either arm. Such studies are therefore included in the estimation process. Bradburn and colleagues undertook simulation studies which revealed that all risk difference methods yield confidence intervals that are too wide when events are rare, and have associated poor statistical power, which make them unsuitable for meta-analysis of rare events (Bradburn et al 2007). This is especially relevant when outcomes that focus on treatment safety are being studied, as the ability to identify correctly (or attempt to refute) serious adverse events is a key issue in drug development.

It is likely that outcomes for which no events occur in either arm may not be mentioned in reports of many randomized trials, precluding their inclusion in a meta-analysis. It is unclear, though, when working with published results, whether failure to mention a particular adverse event means there were no such events, or simply that such events were not included as a measured endpoint. Whilst the results of risk difference meta-analyses will be affected by non-reporting of outcomes with no events, odds and risk ratio based methods naturally exclude these data whether or not they are published, and are therefore unaffected.

10.4.4.3 Validity of methods of meta-analysis for rare events

Simulation studies have revealed that many meta-analytical methods can give misleading results for rare events, which is unsurprising given their reliance on asymptotic statistical theory. Their performance has been judged suboptimal either through results being biased, confidence intervals being inappropriately wide, or statistical power being too low to detect substantial differences.

In the following we consider the choice of statistical method for meta-analyses of odds ratios. Appropriate choices appear to depend on the comparator group risk, the likely size of the treatment effect and consideration of balance in the numbers of experimental and comparator participants in the constituent studies. We are not aware of research that has evaluated risk ratio measures directly, but their performance is likely to be very similar to corresponding odds ratio measurements. When events are rare, estimates of odds and risks are near identical, and results of both can be interpreted as ratios of probabilities.

Bradburn and colleagues found that many of the most commonly used meta-analytical methods were biased when events were rare (Bradburn et al 2007). The bias was greatest in inverse variance and DerSimonian and Laird odds ratio and risk difference methods, and the Mantel-Haenszel odds ratio method using a 0.5 zero-cell correction. As already noted, risk difference meta-analytical methods tended to show conservative confidence interval coverage and low statistical power when risks of events were low.

At event rates below 1% the Peto one-step odds ratio method was found to be the least biased and most powerful method, and provided the best confidence interval coverage, provided there was no substantial imbalance between treatment and comparator group sizes within studies, and treatment effects were not exceptionally large. This finding was consistently observed across three different meta-analytical scenarios, and was also observed by Sweeting and colleagues (Sweeting et al 2004).

This finding was noted despite the method producing only an approximation to the odds ratio. For very large effects (e.g. risk ratio=0.2) when the approximation is known to be poor, treatment effects were under-estimated, but the Peto method still had the best performance of all the methods considered for event risks of 1 in 1000, and the bias was never more than 6% of the comparator group risk.

In other circumstances (i.e. event risks above 1%, very large effects at event risks around 1%, and meta-analyses where many studies were substantially imbalanced) the best performing methods were the Mantel-Haenszel odds ratio without zero-cell corrections, logistic regression and an exact method. None of these methods is available in RevMan.

Methods that should be avoided with rare events are the inverse-variance methods (including the DerSimonian and Laird random-effects method) (Efthimiou 2018). These directly incorporate the study’s variance in the estimation of its contribution to the meta-analysis, but these are usually based on a large-sample variance approximation, which was not intended for use with rare events. We would suggest that incorporation of heterogeneity into an estimate of a treatment effect should be a secondary consideration when attempting to produce estimates of effects from sparse data – the primary concern is to discern whether there is any signal of an effect in the data.

10.5 Meta-analysis of continuous outcomes

An important assumption underlying standard methods for meta-analysis of continuous data is that the outcomes have a normal distribution in each intervention arm in each study. This assumption may not always be met, although it is unimportant in very large studies. It is useful to consider the possibility of skewed data (see Section 10.5.3 ).

10.5.1 Which effect measure for continuous outcomes?

The two summary statistics commonly used for meta-analysis of continuous data are the mean difference (MD) and the standardized mean difference (SMD). Other options are available, such as the ratio of means (see Chapter 6, Section 6.5.1 ). Selection of summary statistics for continuous data is principally determined by whether studies all report the outcome using the same scale (when the mean difference can be used) or using different scales (when the standardized mean difference is usually used). The ratio of means can be used in either situation, but is appropriate only when outcome measurements are strictly greater than zero. Further considerations in deciding on an effect measure that will facilitate interpretation of the findings appears in Chapter 15, Section 15.5 .

The different roles played in MD and SMD approaches by the standard deviations (SDs) of outcomes observed in the two groups should be understood.

For the mean difference approach, the SDs are used together with the sample sizes to compute the weight given to each study. Studies with small SDs are given relatively higher weight whilst studies with larger SDs are given relatively smaller weights. This is appropriate if variation in SDs between studies reflects differences in the reliability of outcome measurements, but is probably not appropriate if the differences in SD reflect real differences in the variability of outcomes in the study populations.

For the standardized mean difference approach, the SDs are used to standardize the mean differences to a single scale, as well as in the computation of study weights. Thus, studies with small SDs lead to relatively higher estimates of SMD, whilst studies with larger SDs lead to relatively smaller estimates of SMD. For this to be appropriate, it must be assumed that between-study variation in SDs reflects only differences in measurement scales and not differences in the reliability of outcome measures or variability among study populations, as discussed in Chapter 6, Section 6.5.1.2 .

These assumptions of the methods should be borne in mind when unexpected variation of SDs is observed across studies.

10.5.2 Meta-analysis of change scores

In some circumstances an analysis based on changes from baseline will be more efficient and powerful than comparison of post-intervention values, as it removes a component of between-person variability from the analysis. However, calculation of a change score requires measurement of the outcome twice and in practice may be less efficient for outcomes that are unstable or difficult to measure precisely, where the measurement error may be larger than true between-person baseline variability. Change-from-baseline outcomes may also be preferred if they have a less skewed distribution than post-intervention measurement outcomes. Although sometimes used as a device to ‘correct’ for unlucky randomization, this practice is not recommended.

The preferred statistical approach to accounting for baseline measurements of the outcome variable is to include the baseline outcome measurements as a covariate in a regression model or analysis of covariance (ANCOVA). These analyses produce an ‘adjusted’ estimate of the intervention effect together with its standard error. These analyses are the least frequently encountered, but as they give the most precise and least biased estimates of intervention effects they should be included in the analysis when they are available. However, they can only be included in a meta-analysis using the generic inverse-variance method, since means and SDs are not available for each intervention group separately.

In practice an author is likely to discover that the studies included in a review include a mixture of change-from-baseline and post-intervention value scores. However, mixing of outcomes is not a problem when it comes to meta-analysis of MDs. There is no statistical reason why studies with change-from-baseline outcomes should not be combined in a meta-analysis with studies with post-intervention measurement outcomes when using the (unstandardized) MD method. In a randomized study, MD based on changes from baseline can usually be assumed to be addressing exactly the same underlying intervention effects as analyses based on post-intervention measurements. That is to say, the difference in mean post-intervention values will on average be the same as the difference in mean change scores. If the use of change scores does increase precision, appropriately, the studies presenting change scores will be given higher weights in the analysis than they would have received if post-intervention values had been used, as they will have smaller SDs.

When combining the data on the MD scale, authors must be careful to use the appropriate means and SDs (either of post-intervention measurements or of changes from baseline) for each study. Since the mean values and SDs for the two types of outcome may differ substantially, it may be advisable to place them in separate subgroups to avoid confusion for the reader, but the results of the subgroups can legitimately be pooled together.

In contrast, post-intervention value and change scores should not in principle be combined using standard meta-analysis approaches when the effect measure is an SMD. This is because the SDs used in the standardization reflect different things. The SD when standardizing post-intervention values reflects between-person variability at a single point in time. The SD when standardizing change scores reflects variation in between-person changes over time, so will depend on both within-person and between-person variability; within-person variability in turn is likely to depend on the length of time between measurements. Nevertheless, an empirical study of 21 meta-analyses in osteoarthritis did not find a difference between combined SMDs based on post-intervention values and combined SMDs based on change scores (da Costa et al 2013). One option is to standardize SMDs using post-intervention SDs rather than change score SDs. This would lead to valid synthesis of the two approaches, but we are not aware that an appropriate standard error for this has been derived.

A common practical problem associated with including change-from-baseline measures is that the SD of changes is not reported. Imputation of SDs is discussed in Chapter 6, Section 6.5.2.8 .

10.5.3 Meta-analysis of skewed data

Analyses based on means are appropriate for data that are at least approximately normally distributed, and for data from very large trials. If the true distribution of outcomes is asymmetrical, then the data are said to be skewed. Review authors should consider the possibility and implications of skewed data when analysing continuous outcomes (see MECIR Box 10.5.a ). Skew can sometimes be diagnosed from the means and SDs of the outcomes. A rough check is available, but it is only valid if a lowest or highest possible value for an outcome is known to exist. Thus, the check may be used for outcomes such as weight, volume and blood concentrations, which have lowest possible values of 0, or for scale outcomes with minimum or maximum scores, but it may not be appropriate for change-from-baseline measures. The check involves calculating the observed mean minus the lowest possible value (or the highest possible value minus the observed mean), and dividing this by the SD. A ratio less than 2 suggests skew (Altman and Bland 1996). If the ratio is less than 1, there is strong evidence of a skewed distribution.

Transformation of the original outcome data may reduce skew substantially. Reports of trials may present results on a transformed scale, usually a log scale. Collection of appropriate data summaries from the trialists, or acquisition of individual patient data, is currently the approach of choice. Appropriate data summaries and analysis strategies for the individual patient data will depend on the situation. Consultation with a knowledgeable statistician is advised.

Where data have been analysed on a log scale, results are commonly presented as geometric means and ratios of geometric means. A meta-analysis may be then performed on the scale of the log-transformed data; an example of the calculation of the required means and SD is given in Chapter 6, Section 6.5.2.4 . This approach depends on being able to obtain transformed data for all studies; methods for transforming from one scale to the other are available (Higgins et al 2008b). Log-transformed and untransformed data should not be mixed in a meta-analysis.

MECIR Box 10.5.a Relevant expectations for conduct of intervention reviews

10.6 Combining dichotomous and continuous outcomes

Occasionally authors encounter a situation where data for the same outcome are presented in some studies as dichotomous data and in other studies as continuous data. For example, scores on depression scales can be reported as means, or as the percentage of patients who were depressed at some point after an intervention (i.e. with a score above a specified cut-point). This type of information is often easier to understand, and more helpful, when it is dichotomized. However, deciding on a cut-point may be arbitrary, and information is lost when continuous data are transformed to dichotomous data.

There are several options for handling combinations of dichotomous and continuous data. Generally, it is useful to summarize results from all the relevant, valid studies in a similar way, but this is not always possible. It may be possible to collect missing data from investigators so that this can be done. If not, it may be useful to summarize the data in three ways: by entering the means and SDs as continuous outcomes, by entering the counts as dichotomous outcomes and by entering all of the data in text form as ‘Other data’ outcomes.

There are statistical approaches available that will re-express odds ratios as SMDs (and vice versa), allowing dichotomous and continuous data to be combined (Anzures-Cabrera et al 2011). A simple approach is as follows. Based on an assumption that the underlying continuous measurements in each intervention group follow a logistic distribution (which is a symmetrical distribution similar in shape to the normal distribution, but with more data in the distributional tails), and that the variability of the outcomes is the same in both experimental and comparator participants, the odds ratios can be re-expressed as a SMD according to the following simple formula (Chinn 2000):

The standard error of the log odds ratio can be converted to the standard error of a SMD by multiplying by the same constant (√3/π=0.5513). Alternatively SMDs can be re-expressed as log odds ratios by multiplying by π/√3=1.814. Once SMDs (or log odds ratios) and their standard errors have been computed for all studies in the meta-analysis, they can be combined using the generic inverse-variance method. Standard errors can be computed for all studies by entering the data as dichotomous and continuous outcome type data, as appropriate, and converting the confidence intervals for the resulting log odds ratios and SMDs into standard errors (see Chapter 6, Section 6.3 ).

10.7 Meta-analysis of ordinal outcomes and measurement scale s

Ordinal and measurement scale outcomes are most commonly meta-analysed as dichotomous data (if so, see Section 10.4 ) or continuous data (if so, see Section 10.5 ) depending on the way that the study authors performed the original analyses.

Occasionally it is possible to analyse the data using proportional odds models. This is the case when ordinal scales have a small number of categories, the numbers falling into each category for each intervention group can be obtained, and the same ordinal scale has been used in all studies. This approach may make more efficient use of all available data than dichotomization, but requires access to statistical software and results in a summary statistic for which it is challenging to find a clinical meaning.

The proportional odds model uses the proportional odds ratio as the measure of intervention effect (Agresti 1996) (see Chapter 6, Section 6.6 ), and can be used for conducting a meta-analysis in advanced statistical software packages (Whitehead and Jones 1994). Estimates of log odds ratios and their standard errors from a proportional odds model may be meta-analysed using the generic inverse-variance method (see Section 10.3.3 ). If the same ordinal scale has been used in all studies, but in some reports has been presented as a dichotomous outcome, it may still be possible to include all studies in the meta-analysis. In the context of the three-category model, this might mean that for some studies category 1 constitutes a success, while for others both categories 1 and 2 constitute a success. Methods are available for dealing with this, and for combining data from scales that are related but have different definitions for their categories (Whitehead and Jones 1994).

10.8 Meta-analysis of counts and rates

Results may be expressed as count data when each participant may experience an event, and may experience it more than once (see Chapter 6, Section 6.7 ). For example, ‘number of strokes’, or ‘number of hospital visits’ are counts. These events may not happen at all, but if they do happen there is no theoretical maximum number of occurrences for an individual. Count data may be analysed using methods for dichotomous data if the counts are dichotomized for each individual (see Section 10.4 ), continuous data (see Section 10.5 ) and time-to-event data (see Section 10.9 ), as well as being analysed as rate data.

Rate data occur if counts are measured for each participant along with the time over which they are observed. This is particularly appropriate when the events being counted are rare. For example, a woman may experience two strokes during a follow-up period of two years. Her rate of strokes is one per year of follow-up (or, equivalently 0.083 per month of follow-up). Rates are conventionally summarized at the group level. For example, participants in the comparator group of a clinical trial may experience 85 strokes during a total of 2836 person-years of follow-up. An underlying assumption associated with the use of rates is that the risk of an event is constant across participants and over time. This assumption should be carefully considered for each situation. For example, in contraception studies, rates have been used (known as Pearl indices) to describe the number of pregnancies per 100 women-years of follow-up. This is now considered inappropriate since couples have different risks of conception, and the risk for each woman changes over time. Pregnancies are now analysed more often using life tables or time-to-event methods that investigate the time elapsing before the first pregnancy.

Analysing count data as rates is not always the most appropriate approach and is uncommon in practice. This is because:

• the assumption of a constant underlying risk may not be suitable; and
• the statistical methods are not as well developed as they are for other types of data.

The results of a study may be expressed as a rate ratio , that is the ratio of the rate in the experimental intervention group to the rate in the comparator group. The (natural) logarithms of the rate ratios may be combined across studies using the generic inverse-variance method (see Section 10.3.3 ). Alternatively, Poisson regression approaches can be used (Spittal et al 2015).

In a randomized trial, rate ratios may often be very similar to risk ratios obtained after dichotomizing the participants, since the average period of follow-up should be similar in all intervention groups. Rate ratios and risk ratios will differ, however, if an intervention affects the likelihood of some participants experiencing multiple events.

It is possible also to focus attention on the rate difference (see Chapter 6, Section 6.7.1 ). The analysis again can be performed using the generic inverse-variance method (Hasselblad and McCrory 1995, Guevara et al 2004).

10.9 Meta-analysis of time-to-event outcomes

Two approaches to meta-analysis of time-to-event outcomes are readily available to Cochrane Review authors. The choice of which to use will depend on the type of data that have been extracted from the primary studies, or obtained from re-analysis of individual participant data.

If ‘O – E’ and ‘V’ statistics have been obtained (see Chapter 6, Section 6.8.2 ), either through re-analysis of individual participant data or from aggregate statistics presented in the study reports, then these statistics may be entered directly into RevMan using the ‘O – E and Variance’ outcome type. There are several ways to calculate these ‘O – E’ and ‘V’ statistics. Peto’s method applied to dichotomous data (Section 10.4.2 ) gives rise to an odds ratio; a log-rank approach gives rise to a hazard ratio; and a variation of the Peto method for analysing time-to-event data gives rise to something in between (Simmonds et al 2011). The appropriate effect measure should be specified. Only fixed-effect meta-analysis methods are available in RevMan for ‘O – E and Variance’ outcomes.

Alternatively, if estimates of log hazard ratios and standard errors have been obtained from results of Cox proportional hazards regression models, study results can be combined using generic inverse-variance methods (see Section 10.3.3 ).

If a mixture of log-rank and Cox model estimates are obtained from the studies, all results can be combined using the generic inverse-variance method, as the log-rank estimates can be converted into log hazard ratios and standard errors using the approaches discussed in Chapter 6, Section 6.8 .

10.10 Heterogeneity

10.10.1 what is heterogeneity.

Inevitably, studies brought together in a systematic review will differ. Any kind of variability among studies in a systematic review may be termed heterogeneity. It can be helpful to distinguish between different types of heterogeneity. Variability in the participants, interventions and outcomes studied may be described as clinical diversity (sometimes called clinical heterogeneity), and variability in study design, outcome measurement tools and risk of bias may be described as methodological diversity (sometimes called methodological heterogeneity). Variability in the intervention effects being evaluated in the different studies is known as statistical heterogeneity , and is a consequence of clinical or methodological diversity, or both, among the studies. Statistical heterogeneity manifests itself in the observed intervention effects being more different from each other than one would expect due to random error (chance) alone. We will follow convention and refer to statistical heterogeneity simply as heterogeneity .

Clinical variation will lead to heterogeneity if the intervention effect is affected by the factors that vary across studies; most obviously, the specific interventions or patient characteristics. In other words, the true intervention effect will be different in different studies.

Differences between studies in terms of methodological factors, such as use of blinding and concealment of allocation sequence, or if there are differences between studies in the way the outcomes are defined and measured, may be expected to lead to differences in the observed intervention effects. Significant statistical heterogeneity arising from methodological diversity or differences in outcome assessments suggests that the studies are not all estimating the same quantity, but does not necessarily suggest that the true intervention effect varies. In particular, heterogeneity associated solely with methodological diversity would indicate that the studies suffer from different degrees of bias. Empirical evidence suggests that some aspects of design can affect the result of clinical trials, although this is not always the case. Further discussion appears in Chapter 7 and Chapter 8 .

The scope of a review will largely determine the extent to which studies included in a review are diverse. Sometimes a review will include studies addressing a variety of questions, for example when several different interventions for the same condition are of interest (see also Chapter 11 ) or when the differential effects of an intervention in different populations are of interest. Meta-analysis should only be considered when a group of studies is sufficiently homogeneous in terms of participants, interventions and outcomes to provide a meaningful summary (see MECIR Box 10.10.a. ). It is often appropriate to take a broader perspective in a meta-analysis than in a single clinical trial. A common analogy is that systematic reviews bring together apples and oranges, and that combining these can yield a meaningless result. This is true if apples and oranges are of intrinsic interest on their own, but may not be if they are used to contribute to a wider question about fruit. For example, a meta-analysis may reasonably evaluate the average effect of a class of drugs by combining results from trials where each evaluates the effect of a different drug from the class.

MECIR Box 10.10.a Relevant expectations for conduct of intervention reviews

There may be specific interest in a review in investigating how clinical and methodological aspects of studies relate to their results. Where possible these investigations should be specified a priori (i.e. in the protocol for the systematic review). It is legitimate for a systematic review to focus on examining the relationship between some clinical characteristic(s) of the studies and the size of intervention effect, rather than on obtaining a summary effect estimate across a series of studies (see Section 10.11 ). Meta-regression may best be used for this purpose, although it is not implemented in RevMan (see Section 10.11.4 ).

10.10.2 Identifying and measuring heterogeneity

It is essential to consider the extent to which the results of studies are consistent with each other (see MECIR Box 10.10.b ). If confidence intervals for the results of individual studies (generally depicted graphically using horizontal lines) have poor overlap, this generally indicates the presence of statistical heterogeneity. More formally, a statistical test for heterogeneity is available. This Chi 2 (χ 2 , or chi-squared) test is included in the forest plots in Cochrane Reviews. It assesses whether observed differences in results are compatible with chance alone. A low P value (or a large Chi 2 statistic relative to its degree of freedom) provides evidence of heterogeneity of intervention effects (variation in effect estimates beyond chance).

MECIR Box 10.10.b Relevant expectations for conduct of intervention reviews

Care must be taken in the interpretation of the Chi 2 test, since it has low power in the (common) situation of a meta-analysis when studies have small sample size or are few in number. This means that while a statistically significant result may indicate a problem with heterogeneity, a non-significant result must not be taken as evidence of no heterogeneity. This is also why a P value of 0.10, rather than the conventional level of 0.05, is sometimes used to determine statistical significance. A further problem with the test, which seldom occurs in Cochrane Reviews, is that when there are many studies in a meta-analysis, the test has high power to detect a small amount of heterogeneity that may be clinically unimportant.

Some argue that, since clinical and methodological diversity always occur in a meta-analysis, statistical heterogeneity is inevitable (Higgins et al 2003). Thus, the test for heterogeneity is irrelevant to the choice of analysis; heterogeneity will always exist whether or not we happen to be able to detect it using a statistical test. Methods have been developed for quantifying inconsistency across studies that move the focus away from testing whether heterogeneity is present to assessing its impact on the meta-analysis. A useful statistic for quantifying inconsistency is:

In this equation, Q is the Chi 2 statistic and df is its degrees of freedom (Higgins and Thompson 2002, Higgins et al 2003). I 2 describes the percentage of the variability in effect estimates that is due to heterogeneity rather than sampling error (chance).

Thresholds for the interpretation of the I 2 statistic can be misleading, since the importance of inconsistency depends on several factors. A rough guide to interpretation in the context of meta-analyses of randomized trials is as follows:

• 0% to 40%: might not be important;
• 30% to 60%: may represent moderate heterogeneity*;
• 50% to 90%: may represent substantial heterogeneity*;
• 75% to 100%: considerable heterogeneity*.

*The importance of the observed value of I 2 depends on (1) magnitude and direction of effects, and (2) strength of evidence for heterogeneity (e.g. P value from the Chi 2 test, or a confidence interval for I 2 : uncertainty in the value of I 2 is substantial when the number of studies is small).

10.10.3 Strategies for addressing heterogeneity

Review authors must take into account any statistical heterogeneity when interpreting results, particularly when there is variation in the direction of effect (see MECIR Box 10.10.c ). A number of options are available if heterogeneity is identified among a group of studies that would otherwise be considered suitable for a meta-analysis.

MECIR Box 10.10.c  Relevant expectations for conduct of intervention reviews

• Check again that the data are correct. Severe apparent heterogeneity can indicate that data have been incorrectly extracted or entered into meta-analysis software. For example, if standard errors have mistakenly been entered as SDs for continuous outcomes, this could manifest itself in overly narrow confidence intervals with poor overlap and hence substantial heterogeneity. Unit-of-analysis errors may also be causes of heterogeneity (see Chapter 6, Section 6.2 ).  
• Do not do a meta -analysis. A systematic review need not contain any meta-analyses. If there is considerable variation in results, and particularly if there is inconsistency in the direction of effect, it may be misleading to quote an average value for the intervention effect.  
• Explore heterogeneity. It is clearly of interest to determine the causes of heterogeneity among results of studies. This process is problematic since there are often many characteristics that vary across studies from which one may choose. Heterogeneity may be explored by conducting subgroup analyses (see Section 10.11.3 ) or meta-regression (see Section 10.11.4 ). Reliable conclusions can only be drawn from analyses that are truly pre-specified before inspecting the studies’ results, and even these conclusions should be interpreted with caution. Explorations of heterogeneity that are devised after heterogeneity is identified can at best lead to the generation of hypotheses. They should be interpreted with even more caution and should generally not be listed among the conclusions of a review. Also, investigations of heterogeneity when there are very few studies are of questionable value.  
• Ignore heterogeneity. Fixed-effect meta-analyses ignore heterogeneity. The summary effect estimate from a fixed-effect meta-analysis is normally interpreted as being the best estimate of the intervention effect. However, the existence of heterogeneity suggests that there may not be a single intervention effect but a variety of intervention effects. Thus, the summary fixed-effect estimate may be an intervention effect that does not actually exist in any population, and therefore have a confidence interval that is meaningless as well as being too narrow (see Section 10.10.4 ).  
• Perform a random-effects meta-analysis. A random-effects meta-analysis may be used to incorporate heterogeneity among studies. This is not a substitute for a thorough investigation of heterogeneity. It is intended primarily for heterogeneity that cannot be explained. An extended discussion of this option appears in Section 10.10.4 .  
• Reconsider the effect measure. Heterogeneity may be an artificial consequence of an inappropriate choice of effect measure. For example, when studies collect continuous outcome data using different scales or different units, extreme heterogeneity may be apparent when using the mean difference but not when the more appropriate standardized mean difference is used. Furthermore, choice of effect measure for dichotomous outcomes (odds ratio, risk ratio, or risk difference) may affect the degree of heterogeneity among results. In particular, when comparator group risks vary, homogeneous odds ratios or risk ratios will necessarily lead to heterogeneous risk differences, and vice versa. However, it remains unclear whether homogeneity of intervention effect in a particular meta-analysis is a suitable criterion for choosing between these measures (see also Section 10.4.3 ).  
• Exclude studies. Heterogeneity may be due to the presence of one or two outlying studies with results that conflict with the rest of the studies. In general it is unwise to exclude studies from a meta-analysis on the basis of their results as this may introduce bias. However, if an obvious reason for the outlying result is apparent, the study might be removed with more confidence. Since usually at least one characteristic can be found for any study in any meta-analysis which makes it different from the others, this criterion is unreliable because it is all too easy to fulfil. It is advisable to perform analyses both with and without outlying studies as part of a sensitivity analysis (see Section 10.14 ). Whenever possible, potential sources of clinical diversity that might lead to such situations should be specified in the protocol.

10.10.4 Incorporating heterogeneity into random-effects models

The random-effects meta-analysis approach incorporates an assumption that the different studies are estimating different, yet related, intervention effects (DerSimonian and Laird 1986, Borenstein et al 2010). The approach allows us to address heterogeneity that cannot readily be explained by other factors. A random-effects meta-analysis model involves an assumption that the effects being estimated in the different studies follow some distribution. The model represents our lack of knowledge about why real, or apparent, intervention effects differ, by considering the differences as if they were random. The centre of the assumed distribution describes the average of the effects, while its width describes the degree of heterogeneity. The conventional choice of distribution is a normal distribution. It is difficult to establish the validity of any particular distributional assumption, and this is a common criticism of random-effects meta-analyses. The importance of the assumed shape for this distribution has not been widely studied.

To undertake a random-effects meta-analysis, the standard errors of the study-specific estimates (SE i in Section 10.3.1 ) are adjusted to incorporate a measure of the extent of variation, or heterogeneity, among the intervention effects observed in different studies (this variation is often referred to as Tau-squared, τ 2 , or Tau 2 ). The amount of variation, and hence the adjustment, can be estimated from the intervention effects and standard errors of the studies included in the meta-analysis.

In a heterogeneous set of studies, a random-effects meta-analysis will award relatively more weight to smaller studies than such studies would receive in a fixed-effect meta-analysis. This is because small studies are more informative for learning about the distribution of effects across studies than for learning about an assumed common intervention effect.

Note that a random-effects model does not ‘take account’ of the heterogeneity, in the sense that it is no longer an issue. It is always preferable to explore possible causes of heterogeneity, although there may be too few studies to do this adequately (see Section 10.11 ).

10.10.4.1 Fixed or random effects?

A fixed-effect meta-analysis provides a result that may be viewed as a ‘typical intervention effect’ from the studies included in the analysis. In order to calculate a confidence interval for a fixed-effect meta-analysis the assumption is usually made that the true effect of intervention (in both magnitude and direction) is the same value in every study (i.e. fixed across studies). This assumption implies that the observed differences among study results are due solely to the play of chance (i.e. that there is no statistical heterogeneity).

A random-effects model provides a result that may be viewed as an ‘average intervention effect’, where this average is explicitly defined according to an assumed distribution of effects across studies. Instead of assuming that the intervention effects are the same, we assume that they follow (usually) a normal distribution. The assumption implies that the observed differences among study results are due to a combination of the play of chance and some genuine variation in the intervention effects.

The random-effects method and the fixed-effect method will give identical results when there is no heterogeneity among the studies.

When heterogeneity is present, a confidence interval around the random-effects summary estimate is wider than a confidence interval around a fixed-effect summary estimate. This will happen whenever the I 2 statistic is greater than zero, even if the heterogeneity is not detected by the Chi 2 test for heterogeneity (see Section 10.10.2 ).

Sometimes the central estimate of the intervention effect is different between fixed-effect and random-effects analyses. In particular, if results of smaller studies are systematically different from results of larger ones, which can happen as a result of publication bias or within-study bias in smaller studies (Egger et al 1997, Poole and Greenland 1999, Kjaergard et al 2001), then a random-effects meta-analysis will exacerbate the effects of the bias (see also Chapter 13, Section 13.3.5.6 ). A fixed-effect analysis will be affected less, although strictly it will also be inappropriate.

The decision between fixed- and random-effects meta-analyses has been the subject of much debate, and we do not provide a universal recommendation. Some considerations in making this choice are as follows:

• Many have argued that the decision should be based on an expectation of whether the intervention effects are truly identical, preferring the fixed-effect model if this is likely and a random-effects model if this is unlikely (Borenstein et al 2010). Since it is generally considered to be implausible that intervention effects across studies are identical (unless the intervention has no effect at all), this leads many to advocate use of the random-effects model.
• Others have argued that a fixed-effect analysis can be interpreted in the presence of heterogeneity, and that it makes fewer assumptions than a random-effects meta-analysis. They then refer to it as a ‘fixed-effects’ meta-analysis (Peto et al 1995, Rice et al 2018).
• Under any interpretation, a fixed-effect meta-analysis ignores heterogeneity. If the method is used, it is therefore important to supplement it with a statistical investigation of the extent of heterogeneity (see Section 10.10.2 ).
• In the presence of heterogeneity, a random-effects analysis gives relatively more weight to smaller studies and relatively less weight to larger studies. If there is additionally some funnel plot asymmetry (i.e. a relationship between intervention effect magnitude and study size), then this will push the results of the random-effects analysis towards the findings in the smaller studies. In the context of randomized trials, this is generally regarded as an unfortunate consequence of the model.
• A pragmatic approach is to plan to undertake both a fixed-effect and a random-effects meta-analysis, with an intention to present the random-effects result if there is no indication of funnel plot asymmetry. If there is an indication of funnel plot asymmetry, then both methods are problematic. It may be reasonable to present both analyses or neither, or to perform a sensitivity analysis in which small studies are excluded or addressed directly using meta-regression (see Chapter 13, Section 13.3.5.6 ).
• The choice between a fixed-effect and a random-effects meta-analysis should never be made on the basis of a statistical test for heterogeneity.

10.10.4.2 Interpretation of random-effects meta-analyses

The summary estimate and confidence interval from a random-effects meta-analysis refer to the centre of the distribution of intervention effects, but do not describe the width of the distribution. Often the summary estimate and its confidence interval are quoted in isolation and portrayed as a sufficient summary of the meta-analysis. This is inappropriate. The confidence interval from a random-effects meta-analysis describes uncertainty in the location of the mean of systematically different effects in the different studies. It does not describe the degree of heterogeneity among studies, as may be commonly believed. For example, when there are many studies in a meta-analysis, we may obtain a very tight confidence interval around the random-effects estimate of the mean effect even when there is a large amount of heterogeneity. A solution to this problem is to consider a prediction interval (see Section 10.10.4.3 ).

Methodological diversity creates heterogeneity through biases variably affecting the results of different studies. The random-effects summary estimate will only correctly estimate the average intervention effect if the biases are symmetrically distributed, leading to a mixture of over-estimates and under-estimates of effect, which is unlikely to be the case. In practice it can be very difficult to distinguish whether heterogeneity results from clinical or methodological diversity, and in most cases it is likely to be due to both, so these distinctions are hard to draw in the interpretation.

When there is little information, either because there are few studies or if the studies are small with few events, a random-effects analysis will provide poor estimates of the amount of heterogeneity (i.e. of the width of the distribution of intervention effects). Fixed-effect methods such as the Mantel-Haenszel method will provide more robust estimates of the average intervention effect, but at the cost of ignoring any heterogeneity.

10.10.4.3 Prediction intervals from a random-effects meta-analysis

An estimate of the between-study variance in a random-effects meta-analysis is typically presented as part of its results. The square root of this number (i.e. Tau) is the estimated standard deviation of underlying effects across studies. Prediction intervals are a way of expressing this value in an interpretable way.

To motivate the idea of a prediction interval, note that for absolute measures of effect (e.g. risk difference, mean difference, standardized mean difference), an approximate 95% range of normally distributed underlying effects can be obtained by creating an interval from 1.96´Tau below the random-effects mean, to 1.96✕Tau above it. (For relative measures such as the odds ratio and risk ratio, an equivalent interval needs to be based on the natural logarithm of the summary estimate.) In reality, both the summary estimate and the value of Tau are associated with uncertainty. A prediction interval seeks to present the range of effects in a way that acknowledges this uncertainty (Higgins et al 2009). A simple 95% prediction interval can be calculated as:

where M is the summary mean from the random-effects meta-analysis, t k −2 is the 95% percentile of a t -distribution with k –2 degrees of freedom, k is the number of studies, Tau 2 is the estimated amount of heterogeneity and SE( M ) is the standard error of the summary mean.

The term ‘prediction interval’ relates to the use of this interval to predict the possible underlying effect in a new study that is similar to the studies in the meta-analysis. A more useful interpretation of the interval is as a summary of the spread of underlying effects in the studies included in the random-effects meta-analysis.

Prediction intervals have proved a popular way of expressing the amount of heterogeneity in a meta-analysis (Riley et al 2011). They are, however, strongly based on the assumption of a normal distribution for the effects across studies, and can be very problematic when the number of studies is small, in which case they can appear spuriously wide or spuriously narrow. Nevertheless, we encourage their use when the number of studies is reasonable (e.g. more than ten) and there is no clear funnel plot asymmetry.

10.10.4.4 Implementing random-effects meta-analyses

As introduced in Section 10.3.2 , the random-effects model can be implemented using an inverse-variance approach, incorporating a measure of the extent of heterogeneity into the study weights. RevMan implements a version of random-effects meta-analysis that is described by DerSimonian and Laird, making use of a ‘moment-based’ estimate of the between-study variance (DerSimonian and Laird 1986). The attraction of this method is that the calculations are straightforward, but it has a theoretical disadvantage in that the confidence intervals are slightly too narrow to encompass full uncertainty resulting from having estimated the degree of heterogeneity.

For many years, RevMan has implemented two random-effects methods for dichotomous data: a Mantel-Haenszel method and an inverse-variance method. Both use the moment-based approach to estimating the amount of between-studies variation. The difference between the two is subtle: the former estimates the between-study variation by comparing each study’s result with a Mantel-Haenszel fixed-effect meta-analysis result, whereas the latter estimates it by comparing each study’s result with an inverse-variance fixed-effect meta-analysis result. In practice, the difference is likely to be trivial.

There are alternative methods for performing random-effects meta-analyses that have better technical properties than the DerSimonian and Laird approach with a moment-based estimate (Veroniki et al 2016). Most notable among these is an adjustment to the confidence interval proposed by Hartung and Knapp and by Sidik and Jonkman (Hartung and Knapp 2001, Sidik and Jonkman 2002). This adjustment widens the confidence interval to reflect uncertainty in the estimation of between-study heterogeneity, and it should be used if available to review authors. An alternative option to encompass full uncertainty in the degree of heterogeneity is to take a Bayesian approach (see Section 10.13 ).

An empirical comparison of different ways to estimate between-study variation in Cochrane meta-analyses has shown that they can lead to substantial differences in estimates of heterogeneity, but seldom have major implications for estimating summary effects (Langan et al 2015). Several simulation studies have concluded that an approach proposed by Paule and Mandel should be recommended (Langan et al 2017); whereas a comprehensive recent simulation study recommended a restricted maximum likelihood approach, although noted that no single approach is universally preferable (Langan et al 2019). Review authors are encouraged to select one of these options if it is available to them.

10.11 Investigating heterogeneity

10.11.1 interaction and effect modification.

Does the intervention effect vary with different populations or intervention characteristics (such as dose or duration)? Such variation is known as interaction by statisticians and as effect modification by epidemiologists. Methods to search for such interactions include subgroup analyses and meta-regression. All methods have considerable pitfalls.

10.11.2 What are subgroup analyses?

Subgroup analyses involve splitting all the participant data into subgroups, often in order to make comparisons between them. Subgroup analyses may be done for subsets of participants (such as males and females), or for subsets of studies (such as different geographical locations). Subgroup analyses may be done as a means of investigating heterogeneous results, or to answer specific questions about particular patient groups, types of intervention or types of study.

Subgroup analyses of subsets of participants within studies are uncommon in systematic reviews based on published literature because sufficient details to extract data about separate participant types are seldom published in reports. By contrast, such subsets of participants are easily analysed when individual participant data have been collected (see Chapter 26 ). The methods we describe in the remainder of this chapter are for subgroups of studies.

Findings from multiple subgroup analyses may be misleading. Subgroup analyses are observational by nature and are not based on randomized comparisons. False negative and false positive significance tests increase in likelihood rapidly as more subgroup analyses are performed. If their findings are presented as definitive conclusions there is clearly a risk of people being denied an effective intervention or treated with an ineffective (or even harmful) intervention. Subgroup analyses can also generate misleading recommendations about directions for future research that, if followed, would waste scarce resources.

It is useful to distinguish between the notions of ‘qualitative interaction’ and ‘quantitative interaction’ (Yusuf et al 1991). Qualitative interaction exists if the direction of effect is reversed, that is if an intervention is beneficial in one subgroup but is harmful in another. Qualitative interaction is rare. This may be used as an argument that the most appropriate result of a meta-analysis is the overall effect across all subgroups. Quantitative interaction exists when the size of the effect varies but not the direction, that is if an intervention is beneficial to different degrees in different subgroups.

10.11.3 Undertaking subgroup analyses

Meta-analyses can be undertaken in RevMan both within subgroups of studies as well as across all studies irrespective of their subgroup membership. It is tempting to compare effect estimates in different subgroups by considering the meta-analysis results from each subgroup separately. This should only be done informally by comparing the magnitudes of effect. Noting that either the effect or the test for heterogeneity in one subgroup is statistically significant whilst that in the other subgroup is not statistically significant does not indicate that the subgroup factor explains heterogeneity. Since different subgroups are likely to contain different amounts of information and thus have different abilities to detect effects, it is extremely misleading simply to compare the statistical significance of the results.

10.11.3.1 Is the effect different in different subgroups?

Valid investigations of whether an intervention works differently in different subgroups involve comparing the subgroups with each other. It is a mistake to compare within-subgroup inferences such as P values. If one subgroup analysis is statistically significant and another is not, then the latter may simply reflect a lack of information rather than a smaller (or absent) effect. When there are only two subgroups, non-overlap of the confidence intervals indicates statistical significance, but note that the confidence intervals can overlap to a small degree and the difference still be statistically significant.

A formal statistical approach should be used to examine differences among subgroups (see MECIR Box 10.11.a ). A simple significance test to investigate differences between two or more subgroups can be performed (Borenstein and Higgins 2013). This procedure consists of undertaking a standard test for heterogeneity across subgroup results rather than across individual study results. When the meta-analysis uses a fixed-effect inverse-variance weighted average approach, the method is exactly equivalent to the test described by Deeks and colleagues (Deeks et al 2001). An I 2 statistic is also computed for subgroup differences. This describes the percentage of the variability in effect estimates from the different subgroups that is due to genuine subgroup differences rather than sampling error (chance). Note that these methods for examining subgroup differences should be used only when the data in the subgroups are independent (i.e. they should not be used if the same study participants contribute to more than one of the subgroups in the forest plot).

If fixed-effect models are used for the analysis within each subgroup, then these statistics relate to differences in typical effects across different subgroups. If random-effects models are used for the analysis within each subgroup, then the statistics relate to variation in the mean effects in the different subgroups.

An alternative method for testing for differences between subgroups is to use meta-regression techniques, in which case a random-effects model is generally preferred (see Section 10.11.4 ). Tests for subgroup differences based on random-effects models may be regarded as preferable to those based on fixed-effect models, due to the high risk of false-positive results when a fixed-effect model is used to compare subgroups (Higgins and Thompson 2004).

MECIR Box 10.11.a Relevant expectations for conduct of intervention reviews

10.11.4 Meta-regression

If studies are divided into subgroups (see Section 10.11.2 ), this may be viewed as an investigation of how a categorical study characteristic is associated with the intervention effects in the meta-analysis. For example, studies in which allocation sequence concealment was adequate may yield different results from those in which it was inadequate. Here, allocation sequence concealment, being either adequate or inadequate, is a categorical characteristic at the study level. Meta-regression is an extension to subgroup analyses that allows the effect of continuous, as well as categorical, characteristics to be investigated, and in principle allows the effects of multiple factors to be investigated simultaneously (although this is rarely possible due to inadequate numbers of studies) (Thompson and Higgins 2002). Meta-regression should generally not be considered when there are fewer than ten studies in a meta-analysis.

Meta-regressions are similar in essence to simple regressions, in which an outcome variable is predicted according to the values of one or more explanatory variables . In meta-regression, the outcome variable is the effect estimate (for example, a mean difference, a risk difference, a log odds ratio or a log risk ratio). The explanatory variables are characteristics of studies that might influence the size of intervention effect. These are often called ‘potential effect modifiers’ or covariates. Meta-regressions usually differ from simple regressions in two ways. First, larger studies have more influence on the relationship than smaller studies, since studies are weighted by the precision of their respective effect estimate. Second, it is wise to allow for the residual heterogeneity among intervention effects not modelled by the explanatory variables. This gives rise to the term ‘random-effects meta-regression’, since the extra variability is incorporated in the same way as in a random-effects meta-analysis (Thompson and Sharp 1999).

The regression coefficient obtained from a meta-regression analysis will describe how the outcome variable (the intervention effect) changes with a unit increase in the explanatory variable (the potential effect modifier). The statistical significance of the regression coefficient is a test of whether there is a linear relationship between intervention effect and the explanatory variable. If the intervention effect is a ratio measure, the log-transformed value of the intervention effect should always be used in the regression model (see Chapter 6, Section 6.1.2.1 ), and the exponential of the regression coefficient will give an estimate of the relative change in intervention effect with a unit increase in the explanatory variable.

Meta-regression can also be used to investigate differences for categorical explanatory variables as done in subgroup analyses. If there are J subgroups, membership of particular subgroups is indicated by using J minus 1 dummy variables (which can only take values of zero or one) in the meta-regression model (as in standard linear regression modelling). The regression coefficients will estimate how the intervention effect in each subgroup differs from a nominated reference subgroup. The P value of each regression coefficient will indicate the strength of evidence against the null hypothesis that the characteristic is not associated with the intervention effect.

Meta-regression may be performed using the ‘metareg’ macro available for the Stata statistical package, or using the ‘metafor’ package for R, as well as other packages.

10.11.5 Selection of study characteristics for subgroup analyses and meta-regression

Authors need to be cautious about undertaking subgroup analyses, and interpreting any that they do. Some considerations are outlined here for selecting characteristics (also called explanatory variables, potential effect modifiers or covariates) that will be investigated for their possible influence on the size of the intervention effect. These considerations apply similarly to subgroup analyses and to meta-regressions. Further details may be obtained elsewhere (Oxman and Guyatt 1992, Berlin and Antman 1994).

10.11.5.1 Ensure that there are adequate studies to justify subgroup analyses and meta-regressions

It is very unlikely that an investigation of heterogeneity will produce useful findings unless there is a substantial number of studies. Typical advice for undertaking simple regression analyses: that at least ten observations (i.e. ten studies in a meta-analysis) should be available for each characteristic modelled. However, even this will be too few when the covariates are unevenly distributed across studies.

10.11.5.2 Specify characteristics in advance

Authors should, whenever possible, pre-specify characteristics in the protocol that later will be subject to subgroup analyses or meta-regression. The plan specified in the protocol should then be followed (data permitting), without undue emphasis on any particular findings (see MECIR Box 10.11.b ). Pre-specifying characteristics reduces the likelihood of spurious findings, first by limiting the number of subgroups investigated, and second by preventing knowledge of the studies’ results influencing which subgroups are analysed. True pre-specification is difficult in systematic reviews, because the results of some of the relevant studies are often known when the protocol is drafted. If a characteristic was overlooked in the protocol, but is clearly of major importance and justified by external evidence, then authors should not be reluctant to explore it. However, such post-hoc analyses should be identified as such.

MECIR Box 10.11.b Relevant expectations for conduct of intervention reviews

10.11.5.3 Select a small number of characteristics

The likelihood of a false-positive result among subgroup analyses and meta-regression increases with the number of characteristics investigated. It is difficult to suggest a maximum number of characteristics to look at, especially since the number of available studies is unknown in advance. If more than one or two characteristics are investigated it may be sensible to adjust the level of significance to account for making multiple comparisons.

10.11.5.4 Ensure there is scientific rationale for investigating each characteristic

Selection of characteristics should be motivated by biological and clinical hypotheses, ideally supported by evidence from sources other than the included studies. Subgroup analyses using characteristics that are implausible or clinically irrelevant are not likely to be useful and should be avoided. For example, a relationship between intervention effect and year of publication is seldom in itself clinically informative, and if identified runs the risk of initiating a post-hoc data dredge of factors that may have changed over time.

Prognostic factors are those that predict the outcome of a disease or condition, whereas effect modifiers are factors that influence how well an intervention works in affecting the outcome. Confusion between prognostic factors and effect modifiers is common in planning subgroup analyses, especially at the protocol stage. Prognostic factors are not good candidates for subgroup analyses unless they are also believed to modify the effect of intervention. For example, being a smoker may be a strong predictor of mortality within the next ten years, but there may not be reason for it to influence the effect of a drug therapy on mortality (Deeks 1998). Potential effect modifiers may include participant characteristics (age, setting), the precise interventions (dose of active intervention, choice of comparison intervention), how the study was done (length of follow-up) or methodology (design and quality).

10.11.5.5 Be aware that the effect of a characteristic may not always be identified

Many characteristics that might have important effects on how well an intervention works cannot be investigated using subgroup analysis or meta-regression. These are characteristics of participants that might vary substantially within studies, but that can only be summarized at the level of the study. An example is age. Consider a collection of clinical trials involving adults ranging from 18 to 60 years old. There may be a strong relationship between age and intervention effect that is apparent within each study. However, if the mean ages for the trials are similar, then no relationship will be apparent by looking at trial mean ages and trial-level effect estimates. The problem is one of aggregating individuals’ results and is variously known as aggregation bias, ecological bias or the ecological fallacy (Morgenstern 1982, Greenland 1987, Berlin et al 2002). It is even possible for the direction of the relationship across studies be the opposite of the direction of the relationship observed within each study.

10.11.5.6 Think about whether the characteristic is closely related to another characteristic (confounded)

The problem of ‘confounding’ complicates interpretation of subgroup analyses and meta-regressions and can lead to incorrect conclusions. Two characteristics are confounded if their influences on the intervention effect cannot be disentangled. For example, if those studies implementing an intensive version of a therapy happened to be the studies that involved patients with more severe disease, then one cannot tell which aspect is the cause of any difference in effect estimates between these studies and others. In meta-regression, co-linearity between potential effect modifiers leads to similar difficulties (Berlin and Antman 1994). Computing correlations between study characteristics will give some information about which study characteristics may be confounded with each other.

10.11.6 Interpretation of subgroup analyses and meta-regressions

Appropriate interpretation of subgroup analyses and meta-regressions requires caution (Oxman and Guyatt 1992).

• Subgroup comparisons are observational. It must be remembered that subgroup analyses and meta-regressions are entirely observational in their nature. These analyses investigate differences between studies. Even if individuals are randomized to one group or other within a clinical trial, they are not randomized to go in one trial or another. Hence, subgroup analyses suffer the limitations of any observational investigation, including possible bias through confounding by other study-level characteristics. Furthermore, even a genuine difference between subgroups is not necessarily due to the classification of the subgroups. As an example, a subgroup analysis of bone marrow transplantation for treating leukaemia might show a strong association between the age of a sibling donor and the success of the transplant. However, this probably does not mean that the age of donor is important. In fact, the age of the recipient is probably a key factor and the subgroup finding would simply be due to the strong association between the age of the recipient and the age of their sibling.  
• Was the analysis pre-specified or post hoc? Authors should state whether subgroup analyses were pre-specified or undertaken after the results of the studies had been compiled (post hoc). More reliance may be placed on a subgroup analysis if it was one of a small number of pre-specified analyses. Performing numerous post-hoc subgroup analyses to explain heterogeneity is a form of data dredging. Data dredging is condemned because it is usually possible to find an apparent, but false, explanation for heterogeneity by considering lots of different characteristics.  
• Is there indirect evidence in support of the findings? Differences between subgroups should be clinically plausible and supported by other external or indirect evidence, if they are to be convincing.  
• Is the magnitude of the difference practically important? If the magnitude of a difference between subgroups will not result in different recommendations for different subgroups, then it may be better to present only the overall analysis results.  
• Is there a statistically significant difference between subgroups? To establish whether there is a different effect of an intervention in different situations, the magnitudes of effects in different subgroups should be compared directly with each other. In particular, statistical significance of the results within separate subgroup analyses should not be compared (see Section 10.11.3.1 ).  
• Are analyses looking at within-study or between-study relationships? For patient and intervention characteristics, differences in subgroups that are observed within studies are more reliable than analyses of subsets of studies. If such within-study relationships are replicated across studies then this adds confidence to the findings.

10.11.7 Investigating the effect of underlying risk

One potentially important source of heterogeneity among a series of studies is when the underlying average risk of the outcome event varies between the studies. The underlying risk of a particular event may be viewed as an aggregate measure of case-mix factors such as age or disease severity. It is generally measured as the observed risk of the event in the comparator group of each study (the comparator group risk, or CGR). The notion is controversial in its relevance to clinical practice since underlying risk represents a summary of both known and unknown risk factors. Problems also arise because comparator group risk will depend on the length of follow-up, which often varies across studies. However, underlying risk has received particular attention in meta-analysis because the information is readily available once dichotomous data have been prepared for use in meta-analyses. Sharp provides a full discussion of the topic (Sharp 2001).

Intuition would suggest that participants are more or less likely to benefit from an effective intervention according to their risk status. However, the relationship between underlying risk and intervention effect is a complicated issue. For example, suppose an intervention is equally beneficial in the sense that for all patients it reduces the risk of an event, say a stroke, to 80% of the underlying risk. Then it is not equally beneficial in terms of absolute differences in risk in the sense that it reduces a 50% stroke rate by 10 percentage points to 40% (number needed to treat=10), but a 20% stroke rate by 4 percentage points to 16% (number needed to treat=25).

Use of different summary statistics (risk ratio, odds ratio and risk difference) will demonstrate different relationships with underlying risk. Summary statistics that show close to no relationship with underlying risk are generally preferred for use in meta-analysis (see Section 10.4.3 ).

Investigating any relationship between effect estimates and the comparator group risk is also complicated by a technical phenomenon known as regression to the mean. This arises because the comparator group risk forms an integral part of the effect estimate. A high risk in a comparator group, observed entirely by chance, will on average give rise to a higher than expected effect estimate, and vice versa. This phenomenon results in a false correlation between effect estimates and comparator group risks. There are methods, which require sophisticated software, that correct for regression to the mean (McIntosh 1996, Thompson et al 1997). These should be used for such analyses, and statistical expertise is recommended.

10.11.8 Dose-response analyses

The principles of meta-regression can be applied to the relationships between intervention effect and dose (commonly termed dose-response), treatment intensity or treatment duration (Greenland and Longnecker 1992, Berlin et al 1993). Conclusions about differences in effect due to differences in dose (or similar factors) are on stronger ground if participants are randomized to one dose or another within a study and a consistent relationship is found across similar studies. While authors should consider these effects, particularly as a possible explanation for heterogeneity, they should be cautious about drawing conclusions based on between-study differences. Authors should be particularly cautious about claiming that a dose-response relationship does not exist, given the low power of many meta-regression analyses to detect genuine relationships.

10.12 Missing data

10.12.1 types of missing data.

There are many potential sources of missing data in a systematic review or meta-analysis (see Table 10.12.a ). For example, a whole study may be missing from the review, an outcome may be missing from a study, summary data may be missing for an outcome, and individual participants may be missing from the summary data. Here we discuss a variety of potential sources of missing data, highlighting where more detailed discussions are available elsewhere in the Handbook .

Whole studies may be missing from a review because they are never published, are published in obscure places, are rarely cited, or are inappropriately indexed in databases. Thus, review authors should always be aware of the possibility that they have failed to identify relevant studies. There is a strong possibility that such studies are missing because of their ‘uninteresting’ or ‘unwelcome’ findings (that is, in the presence of publication bias). This problem is discussed at length in Chapter 13 . Details of comprehensive search methods are provided in Chapter 4 .

Some studies might not report any information on outcomes of interest to the review. For example, there may be no information on quality of life, or on serious adverse effects. It is often difficult to determine whether this is because the outcome was not measured or because the outcome was not reported. Furthermore, failure to report that outcomes were measured may be dependent on the unreported results (selective outcome reporting bias; see Chapter 7, Section 7.2.3.3 ). Similarly, summary data for an outcome, in a form that can be included in a meta-analysis, may be missing. A common example is missing standard deviations (SDs) for continuous outcomes. This is often a problem when change-from-baseline outcomes are sought. We discuss imputation of missing SDs in Chapter 6, Section 6.5.2.8 . Other examples of missing summary data are missing sample sizes (particularly those for each intervention group separately), numbers of events, standard errors, follow-up times for calculating rates, and sufficient details of time-to-event outcomes. Inappropriate analyses of studies, for example of cluster-randomized and crossover trials, can lead to missing summary data. It is sometimes possible to approximate the correct analyses of such studies, for example by imputing correlation coefficients or SDs, as discussed in Chapter 23, Section 23.1 , for cluster-randomized studies and Chapter 23,Section 23.2 , for crossover trials. As a general rule, most methodologists believe that missing summary data (e.g. ‘no usable data’) should not be used as a reason to exclude a study from a systematic review. It is more appropriate to include the study in the review, and to discuss the potential implications of its absence from a meta-analysis.

It is likely that in some, if not all, included studies, there will be individuals missing from the reported results. Review authors are encouraged to consider this problem carefully (see MECIR Box 10.12.a ). We provide further discussion of this problem in Section 10.12.3 ; see also Chapter 8, Section 8.5 .

Missing data can also affect subgroup analyses. If subgroup analyses or meta-regressions are planned (see Section 10.11 ), they require details of the study-level characteristics that distinguish studies from one another. If these are not available for all studies, review authors should consider asking the study authors for more information.

Table 10.12.a Types of missing data in a meta-analysis

MECIR Box 10.12.a Relevant expectations for conduct of intervention reviews

10.12.2 General principles for dealing with missing data

There is a large literature of statistical methods for dealing with missing data. Here we briefly review some key concepts and make some general recommendations for Cochrane Review authors. It is important to think why data may be missing. Statisticians often use the terms ‘missing at random’ and ‘not missing at random’ to represent different scenarios.

Data are said to be ‘missing at random’ if the fact that they are missing is unrelated to actual values of the missing data. For instance, if some quality-of-life questionnaires were lost in the postal system, this would be unlikely to be related to the quality of life of the trial participants who completed the forms. In some circumstances, statisticians distinguish between data ‘missing at random’ and data ‘missing completely at random’, although in the context of a systematic review the distinction is unlikely to be important. Data that are missing at random may not be important. Analyses based on the available data will often be unbiased, although based on a smaller sample size than the original data set.

Data are said to be ‘not missing at random’ if the fact that they are missing is related to the actual missing data. For instance, in a depression trial, participants who had a relapse of depression might be less likely to attend the final follow-up interview, and more likely to have missing outcome data. Such data are ‘non-ignorable’ in the sense that an analysis of the available data alone will typically be biased. Publication bias and selective reporting bias lead by definition to data that are ‘not missing at random’, and attrition and exclusions of individuals within studies often do as well.

The principal options for dealing with missing data are:

• analysing only the available data (i.e. ignoring the missing data);
• imputing the missing data with replacement values, and treating these as if they were observed (e.g. last observation carried forward, imputing an assumed outcome such as assuming all were poor outcomes, imputing the mean, imputing based on predicted values from a regression analysis);
• imputing the missing data and accounting for the fact that these were imputed with uncertainty (e.g. multiple imputation, simple imputation methods (as point 2) with adjustment to the standard error); and
• using statistical models to allow for missing data, making assumptions about their relationships with the available data.

Option 2 is practical in most circumstances and very commonly used in systematic reviews. However, it fails to acknowledge uncertainty in the imputed values and results, typically, in confidence intervals that are too narrow. Options 3 and 4 would require involvement of a knowledgeable statistician.

Five general recommendations for dealing with missing data in Cochrane Reviews are as follows:

• Whenever possible, contact the original investigators to request missing data.
• Make explicit the assumptions of any methods used to address missing data: for example, that the data are assumed missing at random, or that missing values were assumed to have a particular value such as a poor outcome.
• Follow the guidance in Chapter 8 to assess risk of bias due to missing outcome data in randomized trials.
• Perform sensitivity analyses to assess how sensitive results are to reasonable changes in the assumptions that are made (see Section 10.14 ).
• Address the potential impact of missing data on the findings of the review in the Discussion section.

10.12.3 Dealing with missing outcome data from individual participants

Review authors may undertake sensitivity analyses to assess the potential impact of missing outcome data, based on assumptions about the relationship between missingness in the outcome and its true value. Several methods are available (Akl et al 2015). For dichotomous outcomes, Higgins and colleagues propose a strategy involving different assumptions about how the risk of the event among the missing participants differs from the risk of the event among the observed participants, taking account of uncertainty introduced by the assumptions (Higgins et al 2008a). Akl and colleagues propose a suite of simple imputation methods, including a similar approach to that of Higgins and colleagues based on relative risks of the event in missing versus observed participants. Similar ideas can be applied to continuous outcome data (Ebrahim et al 2013, Ebrahim et al 2014). Particular care is required to avoid double counting events, since it can be unclear whether reported numbers of events in trial reports apply to the full randomized sample or only to those who did not drop out (Akl et al 2016).

Although there is a tradition of implementing ‘worst case’ and ‘best case’ analyses clarifying the extreme boundaries of what is theoretically possible, such analyses may not be informative for the most plausible scenarios (Higgins et al 2008a).

10.13 Bayesian approaches to meta-analysis

Bayesian statistics is an approach to statistics based on a different philosophy from that which underlies significance tests and confidence intervals. It is essentially about updating of evidence. In a Bayesian analysis, initial uncertainty is expressed through a prior distribution about the quantities of interest. Current data and assumptions concerning how they were generated are summarized in the likelihood . The posterior distribution for the quantities of interest can then be obtained by combining the prior distribution and the likelihood. The likelihood summarizes both the data from studies included in the meta-analysis (for example, 2×2 tables from randomized trials) and the meta-analysis model (for example, assuming a fixed effect or random effects). The result of the analysis is usually presented as a point estimate and 95% credible interval from the posterior distribution for each quantity of interest, which look much like classical estimates and confidence intervals. Potential advantages of Bayesian analyses are summarized in Box 10.13.a . Bayesian analysis may be performed using WinBUGS software (Smith et al 1995, Lunn et al 2000), within R (Röver 2017), or – for some applications – using standard meta-regression software with a simple trick (Rhodes et al 2016).

A difference between Bayesian analysis and classical meta-analysis is that the interpretation is directly in terms of belief: a 95% credible interval for an odds ratio is that region in which we believe the odds ratio to lie with probability 95%. This is how many practitioners actually interpret a classical confidence interval, but strictly in the classical framework the 95% refers to the long-term frequency with which 95% intervals contain the true value. The Bayesian framework also allows a review author to calculate the probability that the odds ratio has a particular range of values, which cannot be done in the classical framework. For example, we can determine the probability that the odds ratio is less than 1 (which might indicate a beneficial effect of an experimental intervention), or that it is no larger than 0.8 (which might indicate a clinically important effect). It should be noted that these probabilities are specific to the choice of the prior distribution. Different meta-analysts may analyse the same data using different prior distributions and obtain different results. It is therefore important to carry out sensitivity analyses to investigate how the results depend on any assumptions made.

In the context of a meta-analysis, prior distributions are needed for the particular intervention effect being analysed (such as the odds ratio or the mean difference) and – in the context of a random-effects meta-analysis – on the amount of heterogeneity among intervention effects across studies. Prior distributions may represent subjective belief about the size of the effect, or may be derived from sources of evidence not included in the meta-analysis, such as information from non-randomized studies of the same intervention or from randomized trials of other interventions. The width of the prior distribution reflects the degree of uncertainty about the quantity. When there is little or no information, a ‘non-informative’ prior can be used, in which all values across the possible range are equally likely.

Most Bayesian meta-analyses use non-informative (or very weakly informative) prior distributions to represent beliefs about intervention effects, since many regard it as controversial to combine objective trial data with subjective opinion. However, prior distributions are increasingly used for the extent of among-study variation in a random-effects analysis. This is particularly advantageous when the number of studies in the meta-analysis is small, say fewer than five or ten. Libraries of data-based prior distributions are available that have been derived from re-analyses of many thousands of meta-analyses in the Cochrane Database of Systematic Reviews (Turner et al 2012).

Box 10.13.a Some potential advantages of Bayesian meta-analysis

Statistical expertise is strongly recommended for review authors who wish to carry out Bayesian analyses. There are several good texts (Sutton et al 2000, Sutton and Abrams 2001, Spiegelhalter et al 2004).

10.14 Sensitivity analyses

The process of undertaking a systematic review involves a sequence of decisions. Whilst many of these decisions are clearly objective and non-contentious, some will be somewhat arbitrary or unclear. For instance, if eligibility criteria involve a numerical value, the choice of value is usually arbitrary: for example, defining groups of older people may reasonably have lower limits of 60, 65, 70 or 75 years, or any value in between. Other decisions may be unclear because a study report fails to include the required information. Some decisions are unclear because the included studies themselves never obtained the information required: for example, the outcomes of those who were lost to follow-up. Further decisions are unclear because there is no consensus on the best statistical method to use for a particular problem.

It is highly desirable to prove that the findings from a systematic review are not dependent on such arbitrary or unclear decisions by using sensitivity analysis (see MECIR Box 10.14.a ). A sensitivity analysis is a repeat of the primary analysis or meta-analysis in which alternative decisions or ranges of values are substituted for decisions that were arbitrary or unclear. For example, if the eligibility of some studies in the meta-analysis is dubious because they do not contain full details, sensitivity analysis may involve undertaking the meta-analysis twice: the first time including all studies and, second, including only those that are definitely known to be eligible. A sensitivity analysis asks the question, ‘Are the findings robust to the decisions made in the process of obtaining them?’

MECIR Box 10.14.a Relevant expectations for conduct of intervention reviews

There are many decision nodes within the systematic review process that can generate a need for a sensitivity analysis. Examples include:

Searching for studies:

• Should abstracts whose results cannot be confirmed in subsequent publications be included in the review?

Eligibility criteria:

• Characteristics of participants: where a majority but not all people in a study meet an age range, should the study be included?
• Characteristics of the intervention: what range of doses should be included in the meta-analysis?
• Characteristics of the comparator: what criteria are required to define usual care to be used as a comparator group?
• Characteristics of the outcome: what time point or range of time points are eligible for inclusion?
• Study design: should blinded and unblinded outcome assessment be included, or should study inclusion be restricted by other aspects of methodological criteria?

What data should be analysed?

• Time-to-event data: what assumptions of the distribution of censored data should be made?
• Continuous data: where standard deviations are missing, when and how should they be imputed? Should analyses be based on change scores or on post-intervention values?
• Ordinal scales: what cut-point should be used to dichotomize short ordinal scales into two groups?
• Cluster-randomized trials: what values of the intraclass correlation coefficient should be used when trial analyses have not been adjusted for clustering?
• Crossover trials: what values of the within-subject correlation coefficient should be used when this is not available in primary reports?
• All analyses: what assumptions should be made about missing outcomes? Should adjusted or unadjusted estimates of intervention effects be used?

Analysis methods:

• Should fixed-effect or random-effects methods be used for the analysis?
• For dichotomous outcomes, should odds ratios, risk ratios or risk differences be used?
• For continuous outcomes, where several scales have assessed the same dimension, should results be analysed as a standardized mean difference across all scales or as mean differences individually for each scale?

Some sensitivity analyses can be pre-specified in the study protocol, but many issues suitable for sensitivity analysis are only identified during the review process where the individual peculiarities of the studies under investigation are identified. When sensitivity analyses show that the overall result and conclusions are not affected by the different decisions that could be made during the review process, the results of the review can be regarded with a higher degree of certainty. Where sensitivity analyses identify particular decisions or missing information that greatly influence the findings of the review, greater resources can be deployed to try and resolve uncertainties and obtain extra information, possibly through contacting trial authors and obtaining individual participant data. If this cannot be achieved, the results must be interpreted with an appropriate degree of caution. Such findings may generate proposals for further investigations and future research.

Reporting of sensitivity analyses in a systematic review may best be done by producing a summary table. Rarely is it informative to produce individual forest plots for each sensitivity analysis undertaken.

Sensitivity analyses are sometimes confused with subgroup analysis. Although some sensitivity analyses involve restricting the analysis to a subset of the totality of studies, the two methods differ in two ways. First, sensitivity analyses do not attempt to estimate the effect of the intervention in the group of studies removed from the analysis, whereas in subgroup analyses, estimates are produced for each subgroup. Second, in sensitivity analyses, informal comparisons are made between different ways of estimating the same thing, whereas in subgroup analyses, formal statistical comparisons are made across the subgroups.

10.15 Chapter information

Editors: Jonathan J Deeks, Julian PT Higgins, Douglas G Altman; on behalf of the Cochrane Statistical Methods Group

Contributing authors: Douglas Altman, Deborah Ashby, Jacqueline Birks, Michael Borenstein, Marion Campbell, Jonathan Deeks, Matthias Egger, Julian Higgins, Joseph Lau, Keith O’Rourke, Gerta Rücker, Rob Scholten, Jonathan Sterne, Simon Thompson, Anne Whitehead

Acknowledgements: We are grateful to the following for commenting helpfully on earlier drafts: Bodil Als-Nielsen, Deborah Ashby, Jesse Berlin, Joseph Beyene, Jacqueline Birks, Michael Bracken, Marion Campbell, Chris Cates, Wendong Chen, Mike Clarke, Albert Cobos, Esther Coren, Francois Curtin, Roberto D’Amico, Keith Dear, Heather Dickinson, Diana Elbourne, Simon Gates, Paul Glasziou, Christian Gluud, Peter Herbison, Sally Hollis, David Jones, Steff Lewis, Tianjing Li, Joanne McKenzie, Philippa Middleton, Nathan Pace, Craig Ramsey, Keith O’Rourke, Rob Scholten, Guido Schwarzer, Jack Sinclair, Jonathan Sterne, Simon Thompson, Andy Vail, Clarine van Oel, Paula Williamson and Fred Wolf.

Funding: JJD received support from the National Institute for Health Research (NIHR) Birmingham Biomedical Research Centre at the University Hospitals Birmingham NHS Foundation Trust and the University of Birmingham. JPTH is a member of the NIHR Biomedical Research Centre at University Hospitals Bristol NHS Foundation Trust and the University of Bristol. JPTH received funding from National Institute for Health Research Senior Investigator award NF-SI-0617-10145. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health.

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What is meta-analysis?

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• Allison Shorten 1 ,
• Brett Shorten 2
• 1 School of Nursing , Yale University , New Haven, Connecticut , USA
• 2 Informed Health Choices Trust, Wollongong, New South Wales, Australia
• Correspondence to : Dr Allison Shorten Yale University School of Nursing, 100 Church Street South, PO Box 9740, New Haven, CT 06536, USA; allison.shorten{at}yale.edu

https://doi.org/10.1136/eb-2012-101118

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When clinicians begin their search for the best available evidence to inform decision-making, they are usually directed to the top of the ‘evidence pyramid’ to find out whether a systematic review and meta-analysis have been conducted. The Cochrane Library 1 is fast filling with systematic reviews and meta-analyses that aim to answer important clinical questions and provide the most reliable evidence to inform practice and research. So what is meta-analysis and how can it contribute to practice?

The Five-step process

There is debate about the best practice for meta-analysis, however there are five common steps.

Step 1: the research question

A clinical research question is identified and a hypothesis proposed. The likely clinical significance is explained and the study design and analytical plan are justified.

Step 2: systematic review

A systematic review (SR) is specifically designed to address the research question and conducted to identify all studies considered to be both relevant and of sufficiently good quality to warrant inclusion. Often, only studies published in established journals are identified, but identification of ‘unpublished’ data is important to avoid ‘publication bias’ or exclusion of studies with negative findings. 4 Some meta-analyses only consider randomised control trials (RCTs) in the quest for highest quality evidence. Other types of ‘experimental’ and ‘quasi-experimental’ studies may be included if they satisfy the defined inclusion/exclusion criteria.

Step 3: data extraction

Once studies are selected for inclusion in the meta-analysis, summary data or outcomes are extracted from each study. In addition, sample sizes and measures of data variability for both intervention and control groups are required. Depending on the study and the research question, outcome measures could include numerical measures or categorical measures. For example, differences in scores on a questionnaire or differences in a measurement level such as blood pressure would be reported as a numerical mean. However, differences in the likelihood of being in one category versus another (eg, vaginal birth versus cesarean birth) are usually reported in terms of risk measures such as OR or relative risk (RR).

Step 4: standardisation and weighting studies

Having assembled all the necessary data, the fourth step is to calculate appropriate summary measures from each study for further analysis. These measures are usually called Effect Sizes and represent the difference in average scores between intervention and control groups. For example, the difference in change in blood pressure between study participants who used drug X compared with participants who used a placebo. Since units of measurement typically vary across included studies, they usually need to be ‘standardised’ in order to produce comparable estimates of this effect. When different outcome measures are used, such as when researchers use different tests, standardisation is imperative. Standardisation is achieved by taking, for each study, the mean score for the intervention group, subtracting the mean for the control group and dividing this result by the appropriate measure of variability in that data set.

The results of some studies need to carry more weight than others. Larger studies (as measured by sample sizes) are thought to produce more precise effect size estimates than smaller studies. Second, studies with less data variability, for example, smaller SD or narrower CIs are often regarded as ‘better quality’ in study design. A weighting statistic that seeks to incorporate both these factors, known as inverse variance , is commonly used.

Step 5: final estimates of effect

The final stage is to select and apply an appropriate model to compare Effect Sizes across different studies. The most common models used are Fixed Effects and Random Effects models. Fixed Effects models are based on the ‘assumption that every study is evaluating a common treatment effect’. 5 This means that the assumption is that all studies would estimate the same Effect Size were it not for different levels of sample variability across different studies. In contrast, the Random Effects model ‘assumes that the true treatment effects in the individual studies may be different from each other’. 5 and attempts to allow for this additional source of interstudy variation in Effect Sizes . Whether this latter source of variability is likely to be important is often assessed within the meta-analysis by testing for ‘heterogeneity’.

Forest plot

The final estimates from a meta-analysis are often graphically reported in the form of a ‘Forest Plot’.

In the hypothetical Forest Plot shown in figure 1 , for each study, a horizontal line indicates the standardised Effect Size estimate (the rectangular box in the centre of each line) and 95% CI for the risk ratio used. For each of the studies, drug X reduced the risk of death (the risk ratio is less than 1.0). However, the first study was larger than the other two (the size of the boxes represents the relative weights calculated by the meta-analysis). Perhaps, because of this, the estimates for the two smaller studies were not statistically significant (the lines emanating from their boxes include the value of 1). When all the three studies were combined in the meta-analysis, as represented by the diamond, we get a more precise estimate of the effect of the drug, where the diamond represents both the combined risk ratio estimate and the limits of the 95% CI.

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Hypothetical Forest Plot

Relevance to practice and research

Many Evidence Based Nursing commentaries feature recently published systematic review and meta-analysis because they not only bring new insight or strength to recommendations about the most effective healthcare practices but they also identify where future research should be directed to bridge the gaps or limitations in current evidence. The strength of conclusions from meta-analysis largely depends on the quality of the data available for synthesis. This reflects the quality of individual studies and the systematic review. Meta-analysis does not magically resolve the problem of underpowered or poorly designed studies and clinicians can be frustrated to find that even when a meta-analysis has been conducted, all that the researchers can conclude is that the evidence is weak, there is uncertainty about the effects of treatment and that higher quality research is needed to better inform practice. This is still an important finding and can inform our practice and challenge us to fill the evidence gaps with better quality research in the future.

• ↵ The Cochrane Library . http://www.thecochranelibrary.com/view/0/index.html (accessed 23 Oct 2012).
• Davey Smith G
• Davey Smoth G
• Higgins JPT ,

Competing interests None.

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Examples of Studies  Using Meta-Analysis

Segool, N. S., & Carlsen, J. S. (2008). Efficacy of cognitive-behavioral and pharmacological treatments for children with social anxiety. Depression and Anxiety, 25 , 620-631.

Childhood social anxiety is a common disorder with significant academic and social impairment. The researchers evaluated the effectiveness of cognitive-behavior therapy and pharmacological treatment (selective serotonin reuptake inhibitor [SSRI]). A literature search found 14 studies that met all of the inclusion criteria for the meta-analysis. These studies compared pre- and post-treatment measures of social anxiety core symptoms, peripheral general anxiousness, and measures of social competency and social impairment.   The meta-analysis found that both cognitive behavior therapy and pharmacological treatment successfully reduced the core symptoms of social anxiety and social impairment and reduced the peripheral symptoms of general anxiousness. Both treatments also resulted in moderate improvements in social competence. Implications of these findings for treatment were discussed by the authors.

Example # 2 

Conner, K. R., Pinquart, M., & Holbrook, A. (2008). Meta-analysis of depression and substance use and impairment among cocaine users. Drug and Alcohol Dependence, 98 , 13-23.

It has long been hypothesized that drug and alcohol use is associated with depression and serious impairment. Some treatments attempt to deal with the depression as a route to reducing the substance use. This study evaluated the hypotheses, among cocaine users, of an association of depression with (1) cocaine use and impairment , (2) alcohol use and impairment, and (3) general drug use and impairment. The hypothesis that women compared with men would show a stronger correlation between depression, substance use and impairment was also tested.

Sixty studies were identified in the literature search that met the inclusion criteria for the meta-analysis. As hypothesized, depression was found to be associated with cocaine, alcohol, and general drug use and impairment. The hypothesized relationship of gender to depression, drug and alcohol use, and impairment, however, was not supported.

Anderson, C. A., & Bushman, B. B. (2001). Effects of violent video games on aggressive behavior, aggressive cognition, aggressive affect, physiological arousal, and pro-social behavior: A meta-analytic review of the scientific literature. Psychological Science, 12 , 353-359.

In their literature review, the authors note that half a century of sophisticated research on the effects of exposure to violent movies and television has amply documented that: even brief exposure to media violence brings about significant increases in aggressive behavior; children's repeated exposure to violent programming leads to their increased aggression as adults and; such media violence is a significant risk factor in the real-world violence of youth. We know that television and movies have such effects but, the researchers asked, does playing violent video games have similar effects on increasing aggressive behavior? The research on this question is not as extensive, because this is a more recent phenomenon. Two main questions were examined in this meta-analysis: (1) "Is exposure to violent media games associated with increased aggression?"; (2) "How can such exposure increase aggression?"

An electronic search was conducted of PsycINFO for all years through 2000, using the search terms: (video or computer or arcade) and (game) and (attack or fight or aggress or violence or hostile or anger or pro-social or help). The latter two search terms were included because earlier research suggested that pro-social behavior and violent media are negatively related. The search identified 35 research articles that included 54 independent samples and a total of 4,262 participants. 

The meta-analysis of the results of the 35 articles examined whether there is a reliable association between exposure to violent video games and each of five dependent measures: aggressive behavior; aggressive cognition; aggressive affect; pro-social behavior; physiological arousal.

The results of the meta-analysis showed there was a significant positive relationship between exposure to violent video games and aggressive behavior, aggressive cognition, aggressive affect, and physiological arousal. There was a significant negative relationship with pro-social behavior. 

The researchers concluded that exposure to violence through violent video games poses a public health threat. 

Schneider, L. S., Dagerman, K., & Insel, P. (2005). Risk of death with atypical antipsychotic drug treatment for dementia: meta-analysis of randomized placebo-controlled trials. JAMA: Journal of the American Medical Association, 294 , 1934-1943.

Elderly persons with Alzheimer’s disease are frequently treated with antipsychotic medications for delusions, aggression, and agitation. While the treatments appear to help control those serious problems, there is growing concern that drugs may increase risks for cerebrovascular problems, cognitive deterioration, and even death. 

The main question of this study is whether antipsychotic drugs increase the risk of death for people with dementia.

The meta analysis selected and evaluated published and unpublished studies that, when pooled, totaled 3353 patients randomly assigned to drug treatment and 1757 randomly assigned to placebo.

A slightly higher proportion of deaths (3.5%) occurred in the drug-treated patients than in the placebo controls (2.3%). No other risk differences between the groups were found. The authors concluded that antipsychotic drugs administered to elderly persons may be associated with slightly higher risk of death compared with placebo.

Den Boer, P. C., Wiersma, D., & Van Den Bosch, R. J. (2004). Why is self-help neglected in the treatment of emotional disorders? Psychological Medicine, 34 , 959-971.

Despite high rates of emotional disorders in the population, mental health care is available to only a very few. Some research suggests that self-help strategies such as and self-help groups can be effective for persons with less serious emotional disorders. But the research evidence is not clear as to whether the relatively inexpensive and more readily provided self-help strategies can be helpful for persons with clinically significant emotional disorders.

Treatment literature on anxiety and/or depressive disorder was searched for 1970-2000. Nine characteristics were used to assess methodological quality, and only 14 studies (14 patients) survived the inclusion criteria. The studies included in the meta-analysis were randomized controlled trials.

 Results show a markedly robust effect of bibliotherapy--essentially self-help versions of cognitive behavioral therapy--versus waiting list or no treatment controls, with a mean effect size of .84.  Results also showed the self-help to be as effective as short-duration professional treatment.  

The major weakness of this study is the small number of primary studies that were found and analyzed. However the findings of such strong effects demand serious consideration of these self-help therapies for fairly serious disorders, as a way of making reasonable help more available. At least the results demand more research investigation. 

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Systematic review and meta-analysis to estimate the burden of non-fatal and fatal overdose among people who inject drugs living in the U.S. and comparator countries: 2010 – 2023

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Background People who inject drugs (PWID) have high risk for overdose, but there are no current estimates of overdose rates in this population. We estimated the rates of non-fatal and fatal overdose among PWID living in the U.S. and comparator countries (Canada, Mexico, United Kingdom, Australia), and ratios of non-fatal to fatal overdose, using literature published 01/01/2010 – 09/29/2023.

Methods PubMed, PsychInfo, Embase, and ProQuest databases were systematically searched to identify publications reporting prevalence or rates of recent (past 12 months) non- fatal and fatal overdose among PWID. Non-fatal and fatal overdose rates were meta-analyzed using random effects models. Risk of bias was assessed using an adapted quality assessment tool, and heterogeneity was explored using sensitivity analyses.

Results Our review included 143 records, with 58 contributing unique data to the meta- analysis. Non-fatal and fatal overdose rates among PWID in the U.S. were 32.9 per 100 person- years (PY) (95% CI: 26.4 – 40.9; n=28) and 1.7 per 100 PY (95% CI: 0.9 – 3.2; n=4), respectively. Limiting the analysis to data collected after 2016 yielded a non-fatal rate of 41.0 per 100 PY (95% CI: 32.1 – 52.5; n=16) and a fatal rate of 2.5 per 100 PY (95% CI: 1.4 – 4.3; n=2) in the U.S. An estimated 5% of overdoses among PWID in the U.S. result in death. Among the analyzed countries, Australia had the lowest non-fatal and fatal overdose rates and the largest ratio of non-fatal to fatal overdose.

Conclusion Findings demonstrate substantial burden of non-fatal and fatal overdose among PWID in the U.S. and comparator countries. Scale-up of interventions that prevent overdose mortality and investments in PWID health research are urgently needed.

Competing Interest Statement

The authors have declared no competing interest.

Funding Statement

This study was funded by Centers for Disease Control and Prevention, National Center for National Center for HIV, Viral Hepatitis, STD, and TB Prevention and the National Institutes of Health, National Institute on Drug Abuse

Author Declarations

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

Author Email Addresses Jalissa Y. Shealey: jsheale{at}emory.edu Eric W. Hall: halleri{at}ohsu.edu Therese D. Pigott: tpigott{at}gsu.edu Lexi Rosmarin: arosmar{at}emory.edu Anastasia Carter: amcart5{at}emory.edu Chiquita Cade: cccade{at}emory.edu Nicole Luisi: nluisi{at}emory.edu Heather Bradley: hbradl2{at}emory.edu

Funding: Centers for Disease Control and Prevention, National Center for National Center for HIV, Viral Hepatitis, STD, and TB Prevention and the National Institutes of Health, National Institute on Drug Abuse.

Data Availability

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Resistance of transgenic maize cultivars to mycotoxin production—systematic review and meta-analysis.

1. Introduction

2.1. general findings, 2.2. mycotoxin levels and groups division, 2.3. fum comparison in conventional and transgenic maize, 2.4. afl levels in conventional and transgenic maize, 2.5. don levels in maize, 2.6. zea in non-trangenic and trangenic maize, 3. discussion, 4. conclusions, 5. materials and methods, statistical analysis, supplementary materials, institutional review board statement, informed consent statement, acknowledgments, conflicts of interest.

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Gomes, A.S.d.L.P.B.; Weber, S.H.; Luciano, F.B. Resistance of Transgenic Maize Cultivars to Mycotoxin Production—Systematic Review and Meta-Analysis. Toxins 2024 , 16 , 373. https://doi.org/10.3390/toxins16080373

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Gomes, Ana Silvia de Lara Pires Batista, Saulo Henrique Weber, and Fernando Bittencourt Luciano. 2024. "Resistance of Transgenic Maize Cultivars to Mycotoxin Production—Systematic Review and Meta-Analysis" Toxins 16, no. 8: 373. https://doi.org/10.3390/toxins16080373

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• Open access
• Published: 16 August 2024

Higher body mass index was associated with a lower mortality of idiopathic pulmonary fibrosis: a meta-analysis

• Dengyun Pan 1   na1 ,
• Qi Wang 1   na1 ,
• Bingdi Yan 1 &
• Xiaomin Su 1  

Journal of Health, Population and Nutrition volume  43 , Article number:  124 ( 2024 ) Cite this article

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In the past few years, there has been a notable rise in the incidence and prevalence of idiopathic pulmonary fibrosis (IPF) on a global scale. A considerable body of research has highlighted the ‘obesity paradox,’ suggesting that a higher body mass index (BMI) can confer a protective effect against numerous chronic diseases. However, the relationship between BMI and the risk of mortality in IPF patients remains underexplored in the existing literature. We aim to shed light on this relationship and potentially offer novel insights into prevention strategies for IPF.

We conducted a systematic search of the PubMed, Embase, and Web of Science databases to collect all published studies examining the correlation between Body Mass Index (BMI) and the mortality risk in patients with IPF, up until February 14, 2023. For the synthesis of the findings, we employed random-effects models. The statistical significance of the association between BMI and the mortality risk in IPF patients was evaluated using the hazard ratio (HR), with the 95% Confidence Interval (CI) serving as the metric for effect size.

A total of 14 data sets involving 2080 patients with IPF were included in the meta-analysis. The combined results of the random-effects models were suggestive of a significant association between lower BMI and a higher risk of death (HR = 0.94, 95% CI = 0.91–0.97, P  < 0.001). For baseline BMI, the risk of death from IPF decreased by 6% for each unit increase. The results of the subgroup analysis suggest that geographic location (Asian subgroup: HR = 0.95, 95%CI = 0.93–0.98, P  = 0.001; Western subgroup: HR = 0.91, 95%CI = 0.84–0.98, P  = 0.014), study type (RCS subgroup: HR = 0.95, 95%CI = 0.92–0.98, P  = 0.004; PCS subgroup: HR = 0.89, 95%CI = 0.84–0.94, P  < 0.001), and sample size (< 100 groups: HR = 0.93, 95%CI = 0.87–1.01, P  = 0.079; >100 groups: HR = 0.94, 95%CI = 0.91–0.97, P  < 0.001 ) were not significant influences on heterogeneity. Of the included literature, those with confounding factors corrected and high NOS scores reduced heterogeneity (HR = 0.93, 95%CI = 0.90–0.96, P  < 0.001). Sensitivity analyses showed that the combined results were stable and not significantly altered by individual studies (HR = 0.93 to 0.95, 95% CI = 0.90–0.96 to 0.92–0.98). Egger’s test suggested no significant publication bias in the included studies ( P  = 0.159).

Conclusions

Higher BMI (BMI ≥ 25 kg/m2) is negatively correlated to some extent with the risk of death in IPF patients, and BMI may become a clinical indicator for determining the prognosis of IPF patients.

Introduction

IPF is a chronic, progressive, fibrous interstitial pneumonia of unknown etiology. The currently recognized mechanism of IPF is that it is a chronic inflammatory and abnormal repair process. In persistent microinjury of the alveolar epithelium from multiple causes, abnormal activation of fibroblasts and excessive accumulation of extracellular matrix lead to an abnormal repair process of lung scar formation as the inflammatory response progresses [ 1 , 2 , 3 ]. In the United States, the median age of newly diagnosed patients is 62 years, 54% of whom are men [ 4 ]. The global incidence and prevalence of IPF is between 0.09 and 1.3 per 10,000 people with a rising trend year by year. Compared to other countries studied, the United States, Korea, and Canada have the highest incidence rates, with a median survival of less than 4 years and a worse prognosis than many common cancers [ 5 , 6 ]. Although corresponding epidemiological data are lacking in China, clinical practice has revealed a significant trend of increasing IPF cases in recent years. The etiology of IPF remains unclear. Several studies have identified potential risk factors, including genetic alterations, viral infections, lifestyle habits, environmental influences, and occupational hazards. However, current evidence suggests that IPF is the result of a complex interaction between genetic and environmental factors. In addition, the occurrence of several diseases can increase the incidence of IPF, such as gastroesophageal reflux (GERD) [ 7 , 8 ], diabetes (DM) [ 9 ], and obstructive sleep apnea (OSA) [ 10 ]. Two introduced antifibrotic drugs, pirfenidone and nintedanib, may significantly delay the decline in lung function and reduce the incidence and severity of associated complications [ 6 ]. However, they are not a cure for IPF. Therefore, the continuous exploration of new specific biomarkers and therapeutic targets will become a major trend in the future.

Obesity is a growing global health problem that affects multiple organ systems and is a potentially modifiable factor in many diseases. Studies have shown that overweight or obesity also increases the risk of a number of diseases, such as: hypertension, dyslipidemia, type 2 diabetes mellitus, metabolic syndrome, chronic kidney disease, coronary heart disease, cerebral vascular lesions, gallbladder stones, arthropathies, polycystic ovary syndrome, sleep apnea syndrome, and a number of tumors [ 11 ]. Current research suggests that the mechanisms of action of obesity in IPF may be related to factors such as chronic inflammation, oxidative stress, and insulin resistance, all of which may be associated with obesity-induced ectopic fat deposition. Obesity-induced low-grade aseptic inflammation and over-infiltration of immune cells in adipose tissue is accompanied by a decreased ability of adipose tissue to store lipids, leading to ectopic fat deposition, which accelerates the onset and progression of pulmonary fibrosis [ 12 , 13 ]. However, multiple studies have reported that adipose tissue plays a protective role, which is called the “obesity paradox” [ 14 ]. A French study showed that nearly one-third of IPF patients were malnourished, and the worse the nutritional status of the patients, the worse their prognosis [ 15 ]. Due to the ease of measurement and relatively high acceptance, BMI has been adopted by most research institutes as an indicator of obesity and health status. It has been found that higher BMI increases the risk of IPF, but the degree of pulmonary fibrosis and the risk of death are low relative to patients with lower BMI, and more refined subgroups have been found to be associated with a higher risk of death with lower BMI [ 14 , 16 ]. In addition, in antifibrotic therapy, higher BMI patients also have relatively better treatment outcomes [ 17 ]. However, the existence of an “obesity paradox” in IPF patients is controversial, with some studies finding no correlation between BMI and mortality [ 18 ].

Currently, many research studies have focused on the diagnosis and treatment modalities of IPF, while other risk factors influencing disease pathogenesis and disease prognosis have received less attention. The available studies suggest that BMI and the risk of death from IPF are uncertain [ 19 , 20 , 21 , 22 ].

Therefore, this study systematically reviewed the relevant literature and defined the relationship between BMI and the mortality of IPF, aiming to provide basis for evaluating the prognosis of IPF patients.

Materials and methods

This meta-analysis was planned and conducted according to the Preferred Reporting Items for Systematic Evaluation and Meta-Analysis (PRISMA) list [ 23 ]. In addition, since the included studies were observational in design, we also followed the Meta-analysis of Observational Studies in Epidemiology (MOOSE) guidelines [ 24 ].

Literature search strategy

In this article, a literature search was conducted through PubMed, Embase, and Web of Science databases according to a pre-defined search strategy. The search terms included: “idiopathic pulmonary fibrosis”, “body mass index”, and “BMI”. Subject terms were searched in combination with free terms, adapting the search formula to the characteristics of the database (see Supplementary Tables 1 – 3 for specific search steps of the database). The search was conducted up to February 14, 2023, with no language restrictions. In addition, this study screened references of relevant reviews and included literature in the hope of obtaining more studies that could be used for meta-analysis.

Inclusion and exclusion criteria

The following were eligible for inclusion in this study: (1) the study population was patients diagnosed with IPF; (2) the exposure factor was BMI at baseline; (3) the study reported a hazard ratio (HR) (95% CI) for change in risk of death with a 1 kg/m 2 increase in BMI; and (4) the study type was a prospective or retrospective cohort study.

Meanwhile, we excluded the following: (1) non-thesis studies such as reviews, conference abstracts, and commentaries; (2) studies with acute exacerbation of IPF; (3) for duplicate publications or the same data used in multiple articles, only the one with the most complete study information was included, and the rest were excluded. Two of the authors independently searched all references, and any discrepancies were resolved by all authors on a voting basis.

Data extraction

Two investigators (Xiaomin Su and Dengyun Pan) independently completed the literature screening according to the inclusion and exclusion criteria described above. After identifying the literature to be included in the analysis, they carried out the data extraction exercise independently according to a pre-designed form. For each study, the following information was collected: name of the first author, publication year, region where the study was conducted, study type, basic characteristics of the study population (sample size, sex, age), follow-up time, drugs used to treat IPF, study outcome and correction factors. After both of them finished the above data extraction work, they exchanged audit extraction forms and discussed and resolved any inconsistencies.

Quality assessment

Quality assessment of eligible studies was performed by two researchers (Xiaomin Su and Bingdi Yan) using the Newcastle-Ottawa Quality Assessment Scale (NOS), which is a validated scale for use in non-randomized observational studies [ 25 ]. The evaluation included three aspects of study subject selection, comparability, and exposure. Scores ranged from 0 to 9 points. Depending on the score, they can be classified as low (0–3 points), medium (4–6 points) and high-quality studies (7–9 points).

Statistical analysis

HR and 95% CI were used as effect sizes to assess whether the association between BMI and the risk of death in patients with IPF was statistically significant. Heterogeneity was tested using Cochran’ s Q test and I 2 test. For the Q statistic, P  < 0.05, or I 2  > 50%, indicated significant heterogeneity between studies, and a random-effects model was used for meta-analysis; if P  ≥ 0.05 and I 2  ≤ 50%, heterogeneity was not significant and a fixed-effects model was used [ 26 ].

Subgroup analysis was performed based on geographic location, study type, sample size, whether to correct for confounders, and methodological quality grouping. The effect of individual included studies on the results of the meta-analysis was evaluated for significance using the one-by-one exclusion test. Egger’s test was used to assess whether there was significant publication bias in the included studies [ 27 ]. If significant publication bias existed, the stability of the combined results was assessed using the cut-and-patch method [ 28 ].

The above statistical analysis was done using Stata 12.0 software.

Literature search

A total of 1270 publications (163 in PubMed, 904 in Embase, and 203 in Wen of Science) were searched in electronic databases for this meta-analysis. Two hundred ninety-two duplicates were excluded, and 957 papers that clearly did not meet the inclusion criteria were excluded after browsing the titles and abstracts. Finally, 21 publications were excluded after full-text reading of 8, and the remaining 13 were included in the meta-analysis. The details of literature search are shown in Fig.  1 .

Literature search results and flowchart of the literature screening process

Study characteristics and quality assessment

The characteristics of the participating studies and patients are shown in Table  1 . As of February 14, 2023, a total of 13 papers were included in this meta-analysis. Ten of them were retrospective cohort studies [ 9 , 19 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ] and three were prospective cohort studies [ 20 , 37 , 38 ]. Study publication years range from 2007 to 2022. Nine of these studies were conducted in Asia [ 9 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 38 ], including Saudi Arabia ( n  = 1), China ( n  = 1), Japan ( n  = 6) and Korea ( n  = 1); Five were conducted in Europe [ 20 , 30 , 36 , 37 ], which includes France ( n  = 1), Italy ( n  = 2) and the UK ( n  = 1); One was conducted in the United States ( n  = 1), located in North America. The baseline mean/median BMI values in these studies ranged between 21 and 30 kg/m 2 . Twelve studies assessed the BMI as a continuous variable [ 9 , 19 , 20 , 29 , 31 , 32 , 33 , 35 , 36 , 37 , 38 ], and one as both a continuous variable and a cut-off value [ 34 ]. The 14 data sets included in this study involve a combined total of 2,080 individuals (1657 males and 423 females). The sample size ranged from 44 to 445 cases. Baseline BMI of study subjects was obtained from medical records, and survival status was confirmed by medical records or telephone callbacks. Information on age, treatment protocol study outcomes, and correction factors are shown in Table  1 .

The NOS scores of the included studies ranged from 4 to 8 points. Thus, nine of the included studies were of high-quality [ 9 , 19 , 20 , 29 , 31 , 33 , 34 , 35 , 36 ] and the others were of moderate methodological quality [ 30 , 32 , 37 , 38 ]. The main types of bias in the included studies were recall bias and confounding bias.

Meta regression

Since the study by Nakatsuka et al. [ 30 ]. had data from two cohorts of the study, there were 14 data sets. A forest plot of the association analysis between BMI and the risk of death from IPF is shown in Fig.  2 . The results of the heterogeneity test of the included studies suggested a statistically significant heterogeneity (I 2  = 46.3%, P  = 0.029). And the random effects model was applied, the summary HR for 14 data sets showed that the association between BMI and the risk of death in IPF patients is significant (HR = 0.94, 95%CI = 0.91–0.97, P  < 0.001). For baseline BMI, the risk of death from IPF decreased by 6% for each unit increase.

Forest plot of BMI and risk of death in patients with IPF

Subgroup analysis

The results of the subgroup analysis are shown in Table  2 , based on geographic location, study type, sample size, whether or not to correct for confounding factors, and methodological quality grouping.

The combined results of Asian subgroup (HR = 0.95, 95%CI = 0.93–0.98, P  = 0.001) and Western subgroup (HR = 0.91, 95%CI = 0.84–0.98, P  = 0.014) were statistically significant (Fig.  3 A). Similarly, according to the study type grouping (Fig.  3 B), the combined results of the two subgroups were significantly (RCS subgroup: HR = 0.95, 95%CI = 0.92–0.98, P  = 0.004; PCS subgroup: HR = 0.89, 95%CI = 0.84–0.94, P  < 0.001). However, subgroup analysis of sample size (Fig.  3 C), for < 100 groups, combined results were not meaningful (HR = 0.93, 95%CI = 0.87–1.01, P  = 0.079). In addition, geographic location, study type, and sample size were not influential factors on heterogeneity in any significant way. The grouping scheme of whether to correct for confounding factors and methodological quality grouping was consistent, and the within-group heterogeneity of subgroups was not at a significant level (Fig.  3 D and E ), which indicates that these two factors are sources of heterogeneity. Studies with high multifactor correction or methodological quality had statistically significant combined results (HR = 0.93, 95%CI = 0.90–0.96, P  < 0.001). Furthermore, considering the significant role of Forced Vital Capacity (FVC) in IPF patients, we conducted a subgroup analysis correcting for FVC. The results indicate that the pooled outcomes are statistically significant, regardless of whether FVC adjustments were applied or not (Fig.  3 F).

Subgroup analysis: geographic location ( A ), types of studies ( B ), sample size ( C ), correcting for confounders and methodological quality( D ), quality of studies ( E ), correcting for FVC (F). RCS, Retrospective cohort study; PCS, Prospective cohort study

Sensitivity analysis and publication Bias test

Sensitivity analysis showed that excluding the literature one by one, the value of the change in the combined results was HR (95% CI): 0.93 (0.90, 0.96) to 0.95 (0.92, 0.98), and excluding any one of the studies, the combined results of the remaining studies had a P  < 0.05. Therefore, the combined results were stable and did not change significantly by individual studies (Fig.  4 ).

sensitivity analysis

Egger’s test was used to assess whether there was significant publication bias between studies, and the results showed P  = 0.159 (Fig.  5 ), suggesting that there was no significant publication bias in the included studies.

Egger’s test for detecting publication bias in included studies

IPF is the most common type of (Idiopathic interstitial pneumonias, IIPs) and has a high degree of individual variability in prognosis. IPF is common in patients over 60 years of age, especially in men who smoke. According to epidemiologic data, the prevalence of IPF is increasing year by year, and the prognosis of IPF worsens with age. Currently, the diagnosis of IPF is mainly based on HRCT imaging and histopathological examination. IPF is incurable, and the main clinical methods are to slow down the progression of the disease, improve the quality of life and prolong the survival period through antifibrotic drug treatment and rehabilitation training. Therefore, the search for markers for the diagnosis and treatment of IPF and for predicting prognosis is crucial.

Studies have found that the 6-minute walk test (6MWT) and its alterations were found to be highly correlated with the prognosis of IPF. 1-year mortality was 2.65 times higher in patients with a 6MWT < 250 m than in patients with a 6MWT ≥ 350 m, and 1-year mortality in patients with a 6-month alteration of > 50 m was 4 times higher in patients with a 6-month alteration ≤ 25 m [ 39 ]. Lung function can also play a role in the prognosis of IPF, with the rate of decline in forced vital capacity of percentage prediction (FVC%pred) being more indicative of disease progression and a better predictor of patient prognosis [ 40 ]. In addition, Ley et al [ 41 ] proposed a four-component gender, age, FVC%pred and Diffusing capacity of the lung for carbon monoxide of percentage prediction (DL CO %pred) gender- age-lung function model and a composite physiological index reflecting the degree of pulmonary fibrosis proposed by Wells et al [ 42 ] are also good predictors of IPF prognosis. Currently, the biomarkers identified are Krebs von den lungen 6 (KL-6), Matrix metalloproteinase 7 (MMP-7), chemokines and their ligands, Surfactant associated protein A (SP-A), SP-D and other markers [ 43 ]. However, biomarkers are still relatively unspecific and do not predict disease progression and regression.

Higher BMI has been shown to be a risk factor in IPF and may increase the incidence of IPF [ 44 ]. Alakhras et al [ 19 ] first reported that there was a negative correlation between BMI and mortality, with relatively lower mortality in patients with higher BMI. This was validated by the results of several subsequent studies. However, some studies have also suggested that higher BMI increases their mortality, especially in IPF patients with lung transplantation. Therefore, this view is still highly controversial.

In this study, the exposure levels of BMI were consistent, and meta-analysis indicated that there was a significant linear association between baseline BMI and the risk of death in patients with IPF. The results of the heterogeneity test for the included studies showed that there was statistically significant heterogeneity. Nevertheless, subgroup analyses found that heterogeneity could be avoided by studies that were corrected for confounders or used high methodological quality. The results by the one-by-one exclusion method suggested that the combined results were not dramatically changed by individual studies, and the results were stable. Moreover, the studies we included had no significant publication bias test and were highly credible.

Over the past few decades, BMI has been shown to be a risk factor for a number of diseases, including cardiovascular disease, diabetes, subarachnoid haemorrhage, cerebral haemorrhage, and some cancers [ 45 ]. This has led to active lifestyle interventions aimed at reducing this risk for individuals and populations. However, in recent years, the newly proposed idea of the “obesity paradox” has caused great controversy. This refers to the fact that individuals with relatively higher values of BMI have a better prognosis than those with lower values of BMI, which has been validated in COPD, cardiovascular disease, certain cancers and other diseases [ 46 ].

Alakhras et al. [ 19 ]. were the first to report a significant relationship between BMI and survival in 197 patients with IPF. Three groups (< 25, 25–30, and > 30 kg/m 2 ) were categorized according to BMI, and median survival was 3.6, 3.8, and 5.8 years, respectively. Proportional risk regression showed a significant, independent negative association between baseline BMI and mortality. Yoo et al. [ 35 ]. similarly reported that lower baseline BMI was independently associated with higher three-year mortality among 445 patients with IPF after adjusting for several confounders including the Charlson Comorbidity Index, disease progression, and acute exacerbations. Suzuki et al. [ 34 ]. conducted a cohort study of 208 patients with IPF in two groups receiving antifibrotic therapy with pirfenidone or nintedanib. A significant, negative and independent association with five-year mortality was observed when BMI was considered as a continuous variable and a threshold value of 24.1 kg/m 2 was used. Similarly, Jouneau et al. [ 20 ]. found that patients with a baseline BMI < 25 kg/m 2 , or an annual weight loss of > 0–5% or ≥ 5% may have a poorer prognosis at 1 year than patients with a BMI ≥ 25 kg/m 2 or no weight loss. This negative correlation was also found in a study by Mura et al [ 37 ] (HR = 0.89, 95% CI = 0.80–0.98, p  = 0.0155), but was not corrected for other confounders.

This is consistent with the results of our analysis. BMI and risk of death from IPF were significantly associated. We also found that for baseline BMI, the risk of death from IPF decreased by 6% for each unit increase. This is also consistent with the findings of Alakhras et al. [ 19 ]. (HR = 0.93, 95%CI = 0.89–0.97, P  = 0.002 per 1-U increase in BMI).

Internationally we regard a BMI ≥ 30 kg/m 2 as obese, but the use of this value alone as a criterion to define obesity in many studies is controversial. Body composition variability in patients with the same BMI, such as the co-occurrence of low muscle and high adipose tissue may occur in different subgroups of BMI. The BMI formula does not take into account body composition (muscle mass vs. adipose tissue content) and distribution (visceral fat vs. subcutaneous fat). Other tests such as dual-energy X-ray absorptiometry (DEXA), computed tomography (CT) and MRI are more expressive of obesity typing. But their application is limited by their cost, radiation and the technical expertise required. Therefore, BMI is more widely used and accepted than other tests [ 47 ].

As has been suggested in patients with heart failure, higher BMI in patients with IPF may not be primarily associated with increased fat mass, but rather with increased fat-free mass (muscle mass). This may increase oxygen consumption through increased muscle diffusion, mitochondrial respiratory capacity, and skeletal muscle strength, thereby improving exercise tolerance and cardiorespiratory fitness [ 48 , 49 , 50 , 51 ]. Suzuki et al. [ 34 ]. showed that BMI was remarkably associated with cross-sectional area of elector spine muscles (ESM CSA ) ( r  = 0.500, P  < 0.0001). In COPD this is also known as the muscle mass hypothesis, which states that obese patients are better able to adapt to acute exacerbations due to increased reserves from greater muscle mass [ 52 ]. In addition, respiratory failure is one of the leading causes of death in patients with IPF. This theory of muscle mass loss could also explain the poor prognosis of patients with IPF disease, as patients with better tolerance to muscle mass depletion have a higher chance of survival. Based on this hypothesis, we can assume that metabolically healthy overweight and obese patients with higher muscle mass have a higher chance of recovery than the non-obese population [ 49 ].

Another theory is that of brown adipose tissue and its anti-inflammatory effects on the body. Brown adipose tissue has properties similar to lean body mass, as it decreases the levels of lipopolysaccharides in the body, which stimulate pro-inflammatory cytokines, thus effectively reducing systemic inflammation levels. White adipose tissue functions in the opposite way and can have deleterious effects on the body. A shift from white adipose tissue to brown fat occurs in some obese individuals [ 52 ].

In addition, it may also be a possibility that the interaction between BMI and clinical symptoms in patients with IPF is influenced by disease states, such as heart failure, in which a negative correlation between BMI and poor outcomes has been described [ 53 ].

However, there are still some shortcomings in our study. The sample sizes of the included studies were relatively small, and we need more high-quality, large-sample studies to validate the extrapolation of the results. The included studies were all observational and had many confounders. Although most studies performed multifactorial corrections, the corrections were also not uniform and may have exaggerated the strength of the association between BMI and risk of death. Due to the lack of sufficient original studies, this meta-analysis was unable to quantitatively group the associations between different BMI classes, levels of BMI change, and the risk of death, and it is hoped that subsequent studies will focus on these two parts of the results.

Higher BMI (BMI ≥ 25 kg/m 2 ) is negatively correlated to some extent with the risk of death in IPF patients, and BMI may become a clinical indicator for determining the prognosis of IPF patients.

Data availability

No datasets were generated or analysed during the current study.

Abbreviations

Idiopathic pulmonary fibrosis

Body mass index

Hazard ratio

Gastroesophageal reflux

Obstructive sleep apnea

Preferred reporting items for systematic evaluation and meta-analysis

Meta-analysis of observational studies in epidemiology

Newcastle-ottawa quality assessment scale

Dual-energy X-ray absorptiometry

Computed tomography

Total lung capacity

Forced vital capacity

Diffusing capacity of the lung for carbon monoxide

Gender-age-physiology

Retrospective cohort study

Prospective cohort study

6-min walk test

Proton pump inhibitor

United States of America

The United Kingdom of Great Britain and Northern Ireland

Cross-sectional area of elector spine muscles

Muscle attenuation of elector spine muscles

Azathioprine, Mycophenolate mofetil, Cyclosporine

Aggregate systemic inflammation index

Not reported

Idiopathic interstitial pneumonias

Krebs von den lungen 6

Matrix metalloproteinase 7

Surfactant associated protein A

Forced vital capacity of percentage prediction

Diffusing capacity of the lung for carbon monoxide of percentage prediction

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This work was supported by National Natural Science Foundation of China (Grant No. 82100317), Norman Bethune Program of Jilin University (Grant No. 2022B14), “13th five-year plan” Science and Technology Research Project of Jilin Provincial Department of Education (Grant No. JJKH20190048KJ), the Youth Science and Technology Backbone Training Program of Health Commission of Jilin Province (Grant No. 2019Q003), as well as the Medical and Health Talent Special Project of Jilin Province - National Natural Science Foundation of China Cultivation Project (Grant No. 2019SRCJ013).

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Dengyun Pan, Qi Wang, Bingdi Yan & Xiaomin Su

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Xiaomin Su designed the project, retrieved and analyzed the data, revised manuscript. Dengyun Pan retrieved and analyzed the data, wrote the manuscript. Qi Wang wrote the manuscript. Bingdi Yan revised the manuscript. All authors contributed and approved the final version of the manuscript.

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Pan, D., Wang, Q., Yan, B. et al. Higher body mass index was associated with a lower mortality of idiopathic pulmonary fibrosis: a meta-analysis. J Health Popul Nutr 43 , 124 (2024). https://doi.org/10.1186/s41043-024-00620-5

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Meta-analysis in medical research

The objectives of this paper are to provide an introduction to meta-analysis and to discuss the rationale for this type of research and other general considerations. Methods used to produce a rigorous meta-analysis are highlighted and some aspects of presentation and interpretation of meta-analysis are discussed.

Meta-analysis is a quantitative, formal, epidemiological study design used to systematically assess previous research studies to derive conclusions about that body of research. Outcomes from a meta-analysis may include a more precise estimate of the effect of treatment or risk factor for disease, or other outcomes, than any individual study contributing to the pooled analysis. The examination of variability or heterogeneity in study results is also a critical outcome. The benefits of meta-analysis include a consolidated and quantitative review of a large, and often complex, sometimes apparently conflicting, body of literature. The specification of the outcome and hypotheses that are tested is critical to the conduct of meta-analyses, as is a sensitive literature search. A failure to identify the majority of existing studies can lead to erroneous conclusions; however, there are methods of examining data to identify the potential for studies to be missing; for example, by the use of funnel plots. Rigorously conducted meta-analyses are useful tools in evidence-based medicine. The need to integrate findings from many studies ensures that meta-analytic research is desirable and the large body of research now generated makes the conduct of this research feasible.

Important medical questions are typically studied more than once, often by different research teams in different locations. In many instances, the results of these multiple small studies of an issue are diverse and conflicting, which makes the clinical decision-making difficult. The need to arrive at decisions affecting clinical practise fostered the momentum toward "evidence-based medicine" 1 – 2 . Evidence-based medicine may be defined as the systematic, quantitative, preferentially experimental approach to obtaining and using medical information. Therefore, meta-analysis, a statistical procedure that integrates the results of several independent studies, plays a central role in evidence-based medicine. In fact, in the hierarchy of evidence ( Figure 1 ), where clinical evidence is ranked according to the strength of the freedom from various biases that beset medical research, meta-analyses are in the top. In contrast, animal research, laboratory studies, case series and case reports have little clinical value as proof, hence being in the bottom.

Meta-analysis did not begin to appear regularly in the medical literature until the late 1970s but since then a plethora of meta-analyses have emerged and the growth is exponential over time ( Figure 2 ) 3 . Moreover, it has been shown that meta-analyses are the most frequently cited form of clinical research 4 . The merits and perils of the somewhat mysterious procedure of meta-analysis, however, continue to be debated in the medical community 5 – 8 . The objectives of this paper are to introduce meta-analysis and to discuss the rationale for this type of research and other general considerations.

Meta-Analysis and Systematic Review

Glass first defined meta-analysis in the social science literature as "The statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating the findings" 9 . Meta-analysis is a quantitative, formal, epidemiological study design used to systematically assess the results of previous research to derive conclusions about that body of research. Typically, but not necessarily, the study is based on randomized, controlled clinical trials. Outcomes from a meta-analysis may include a more precise estimate of the effect of treatment or risk factor for disease, or other outcomes, than any individual study contributing to the pooled analysis. Identifying sources of variation in responses; that is, examining heterogeneity of a group of studies, and generalizability of responses can lead to more effective treatments or modifications of management. Examination of heterogeneity is perhaps the most important task in meta-analysis. The Cochrane collaboration has been a long-standing, rigorous, and innovative leader in developing methods in the field 10 . Major contributions include the development of protocols that provide structure for literature search methods, and new and extended analytic and diagnostic methods for evaluating the output of meta-analyses. Use of the methods outlined in the handbook should provide a consistent approach to the conduct of meta-analysis. Moreover, a useful guide to improve reporting of systematic reviews and meta-analyses is the PRISMA (Preferred Reporting Items for Systematic reviews and Meta-analyses) statement that replaced the QUOROM (QUality Of Reporting of Meta-analyses) statement 11 – 13 .

Meta-analyses are a subset of systematic review. A systematic review attempts to collate empirical evidence that fits prespecified eligibility criteria to answer a specific research question. The key characteristics of a systematic review are a clearly stated set of objectives with predefined eligibility criteria for studies; an explicit, reproducible methodology; a systematic search that attempts to identify all studies that meet the eligibility criteria; an assessment of the validity of the findings of the included studies (e.g., through the assessment of risk of bias); and a systematic presentation and synthesis of the attributes and findings from the studies used. Systematic methods are used to minimize bias, thus providing more reliable findings from which conclusions can be drawn and decisions made than traditional review methods 14 , 15 . Systematic reviews need not contain a meta-analysisthere are times when it is not appropriate or possible; however, many systematic reviews contain meta-analyses 16 .

The inclusion of observational medical studies in meta-analyses led to considerable debate over the validity of meta-analytical approaches, as there was necessarily a concern that the observational studies were likely to be subject to unidentified sources of confounding and risk modification 17 . Pooling such findings may not lead to more certain outcomes. Moreover, an empirical study showed that in meta-analyses were both randomized and non-randomized was included, nonrandomized studies tended to show larger treatment effects 18 .

Meta-analyses are conducted to assess the strength of evidence present on a disease and treatment. One aim is to determine whether an effect exists; another aim is to determine whether the effect is positive or negative and, ideally, to obtain a single summary estimate of the effect. The results of a meta-analysis can improve precision of estimates of effect, answer questions not posed by the individual studies, settle controversies arising from apparently conflicting studies, and generate new hypotheses. In particular, the examination of heterogeneity is vital to the development of new hypotheses.

Individual or Aggregated Data

The majority of meta-analyses are based on a series of studies to produce a point estimate of an effect and measures of the precision of that estimate. However, methods have been developed for the meta-analyses to be conducted on data obtained from original trials 19 , 20 . This approach may be considered the "gold standard" in metaanalysis because it offers advantages over analyses using aggregated data, including a greater ability to validate the quality of data and to conduct appropriate statistical analysis. Further, it is easier to explore differences in effect across subgroups within the study population than with aggregated data. The use of standardized individual-level information may help to avoid the problems encountered in meta-analyses of prognostic factors 21 , 22 . It is the best way to obtain a more global picture of the natural history and predictors of risk for major outcomes, such as in scleroderma 23 – 26 .This approach relies on cooperation between researchers who conducted the relevant studies. Researchers who are aware of the potential to contribute or conduct these studies will provide and obtain additional benefits by careful maintenance of original databases and making these available for future studies.

Literature Search

A sound meta-analysis is characterized by a thorough and disciplined literature search. A clear definition of hypotheses to be investigated provides the framework for such an investigation. According to the PRISMA statement, an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes and study design (PICOS) should be provided 11 , 12 . It is important to obtain all relevant studies, because loss of studies can lead to bias in the study. Typically, published papers and abstracts are identified by a computerized literature search of electronic databases that can include PubMed ( www.ncbi.nlm.nih.gov./entrez/query.fcgi ), ScienceDirect ( www.sciencedirect.com ), Scirus ( www.scirus.com/srsapp ), ISI Web of Knowledge ( http://www.isiwebofknowledge.com ), Google Scholar ( http://scholar.google.com ) and CENTRAL (Cochrane Central Register of Controlled Trials, http://www.mrw.interscience.wiley.com/cochrane/cochrane_clcentral_articles_fs.htm ). PRISMA statement recommends that a full electronic search strategy for at least one major database to be presented 12 . Database searches should be augmented with hand searches of library resources for relevant papers, books, abstracts, and conference proceedings. Crosschecking of references, citations in review papers, and communication with scientists who have been working in the relevant field are important methods used to provide a comprehensive search. Communication with pharmaceutical companies manufacturing and distributing test products can be appropriate for studies examining the use of pharmaceutical interventions.

It is not feasible to find absolutely every relevant study on a subject. Some or even many studies may not be published, and those that are might not be indexed in computer-searchable databases. Useful sources for unpublished trials are the clinical trials registers, such as the National Library of Medicine's ClinicalTrials.gov Website. The reviews should attempt to be sensitive; that is, find as many studies as possible, to minimize bias and be efficient. It may be appropriate to frame a hypothesis that considers the time over which a study is conducted or to target a particular subpopulation. The decision whether to include unpublished studies is difficult. Although language of publication can provide a difficulty, it is important to overcome this difficulty, provided that the populations studied are relevant to the hypothesis being tested.

Inclusion or Exclusion Criteria and Potential for Bias

Studies are chosen for meta-analysis based on inclusion criteria. If there is more than one hypothesis to be tested, separate selection criteria should be defined for each hypothesis. Inclusion criteria are ideally defined at the stage of initial development of the study protocol. The rationale for the criteria for study selection used should be clearly stated.

One important potential source of bias in meta-analysis is the loss of trials and subjects. Ideally, all randomized subjects in all studies satisfy all of the trial selection criteria, comply with all the trial procedures, and provide complete data. Under these conditions, an "intention-totreat" analysis is straightforward to implement; that is, statistical analysis is conducted on all subjects that are enrolled in a study rather than those that complete all stages of study considered desirable. Some empirical studies had shown that certain methodological characteristics, such as poor concealment of treatment allocation or no blinding in studies exaggerate treatment effects 27 . Therefore, it is important to critically appraise the quality of studies in order to assess the risk of bias.

The study design, including details of the method of randomization of subjects to treatment groups, criteria for eligibility in the study, blinding, method of assessing the outcome, and handling of protocol deviations are important features defining study quality. When studies are excluded from a meta-analysis, reasons for exclusion should be provided for each excluded study. Usually, more than one assessor decides independently which studies to include or exclude, together with a well-defined checklist and a procedure that is followed when the assessors disagree. Two people familiar with the study topic perform the quality assessment for each study, independently. This is followed by a consensus meeting to discuss the studies excluded or included. Practically, the blinding of reviewers from details of a study such as authorship and journal source is difficult.

Before assessing study quality, a quality assessment protocol and data forms should be developed. The goal of this process is to reduce the risk of bias in the estimate of effect. Quality scores that summarize multiple components into a single number exist but are misleading and unhelpful 28 . Rather, investigators should use individual components of quality assessment and describe trials that do not meet the specified quality standards and probably assess the effect on the overall results by excluding them, as part of the sensitivity analyses.

Further, not all studies are completed, because of protocol failure, treatment failure, or other factors. Nonetheless, missing subjects and studies can provide important evidence. It is desirable to obtain data from all relevant randomized trials, so that the most appropriate analysis can be undertaken. Previous studies have discussed the significance of missing trials to the interpretation of intervention studies in medicine 29 , 30 . Journal editors and reviewers need to be aware of the existing bias toward publishing positive findings and ensure that papers that publish negative or even failed trials be published, as long as these meet the quality guidelines for publication.

There are occasions when authors of the selected papers have chosen different outcome criteria for their main analysis. In practice, it may be necessary to revise the inclusion criteria for a meta-analysis after reviewing all of the studies found through the search strategy. Variation in studies reflects the type of study design used, type and application of experimental and control therapies, whether or not the study was published, and, if published, subjected to peer review, and the definition used for the outcome of interest. There are no standardized criteria for inclusion of studies in meta-analysis. Universal criteria are not appropriate, however, because meta-analysis can be applied to a broad spectrum of topics. Published data in journal papers should also be cross-checked with conference papers to avoid repetition in presented data.

Clearly, unpublished studies are not found by searching the literature. It is possible that published studies are systemically different from unpublished studies; for example, positive trial findings may be more likely to be published. Therefore, a meta-analysis based on literature search results alone may lead to publication bias.

Efforts to minimize this potential bias include working from the references in published studies, searching computerized databases of unpublished material, and investigating other sources of information including conference proceedings, graduate dissertations and clinical trial registers.

Statistical analysis

The most common measures of effect used for dichotomous data are the risk ratio (also called relative risk) and the odds ratio. The dominant method used for continuous data are standardized mean difference (SMD) estimation. Methods used in meta-analysis for post hoc analysis of findings are relatively specific to meta-analysis and include heterogeneity analysis, sensitivity analysis, and evaluation of publication bias.

All methods used should allow for the weighting of studies. The concept of weighting reflects the value of the evidence of any particular study. Usually, studies are weighted according to the inverse of their variance 31 . It is important to recognize that smaller studies, therefore, usually contribute less to the estimates of overall effect. However, well-conducted studies with tight control of measurement variation and sources of confounding contribute more to estimates of overall effect than a study of identical size less well conducted.

One of the foremost decisions to be made when conducting a meta-analysis is whether to use a fixed-effects or a random-effects model. A fixed-effects model is based on the assumption that the sole source of variation in observed outcomes is that occurring within the study; that is, the effect expected from each study is the same. Consequently, it is assumed that the models are homogeneous; there are no differences in the underlying study population, no differences in subject selection criteria, and treatments are applied the same way 32 . Fixed-effect methods used for dichotomous data include most often the Mantel-Haenzel method 33 and the Peto method 34 (only for odds ratios).

Random-effects models have an underlying assumption that a distribution of effects exists, resulting in heterogeneity among study results, known as τ2. Consequently, as software has improved, random-effects models that require greater computing power have become more frequently conducted. This is desirable because the strong assumption that the effect of interest is the same in all studies is frequently untenable. Moreover, the fixed effects model is not appropriate when statistical heterogeneity (τ2) is present in the results of studies in the meta-analysis. In the random-effects model, studies are weighted with the inverse of their variance and the heterogeneity parameter. Therefore, it is usually a more conservative approach with wider confidence intervals than the fixed-effects model where the studies are weighted only with the inverse of their variance. The most commonly used random-effects method is the DerSimonian and Laird method 35 . Furthermore, it is suggested that comparing the fixed-effects and random-effect models developed as this process can yield insights to the data 36 .

Heterogeneity

Arguably, the greatest benefit of conducting metaanalysis is to examine sources of heterogeneity, if present, among studies. If heterogeneity is present, the summary measure must be interpreted with caution 37 . When heterogeneity is present, one should question whether and how to generalize the results. Understanding sources of heterogeneity will lead to more effective targeting of prevention and treatment strategies and will result in new research topics being identified. Part of the strategy in conducting a meta-analysis is to identify factors that may be significant determinants of subpopulation analysis or covariates that may be appropriate to explore in all studies.

To understand the nature of variability in studies, it is important to distinguish between different sources of heterogeneity. Variability in the participants, interventions, and outcomes studied has been described as clinical diversity, and variability in study design and risk of bias has been described as methodological diversity 10 . Variability in the intervention effects being evaluated among the different studies is known as statistical heterogeneity and is a consequence of clinical or methodological diversity, or both, among the studies. Statistical heterogeneity manifests itself in the observed intervention effects varying by more than the differences expected among studies that would be attributable to random error alone. Usually, in the literature, statistical heterogeneity is simply referred to as heterogeneity.

Clinical variation will cause heterogeneity if the intervention effect is modified by the factors that vary across studies; most obviously, the specific interventions or participant characteristics that are often reflected in different levels of risk in the control group when the outcome is dichotomous. In other words, the true intervention effect will differ for different studies. Differences between studies in terms of methods used, such as use of blinding or differences between studies in the definition or measurement of outcomes, may lead to differences in observed effects. Significant statistical heterogeneity arising from differences in methods used or differences in outcome assessments suggests that the studies are not all estimating the same effect, but does not necessarily suggest that the true intervention effect varies. In particular, heterogeneity associated solely with methodological diversity indicates that studies suffer from different degrees of bias. Empirical evidence suggests that some aspects of design can affect the result of clinical trials, although this may not always be the case.

The scope of a meta-analysis will largely determine the extent to which studies included in a review are diverse. Meta-analysis should be conducted when a group of studies is sufficiently homogeneous in terms of subjects involved, interventions, and outcomes to provide a meaningful summary. However, it is often appropriate to take a broader perspective in a meta-analysis than in a single clinical trial. Combining studies that differ substantially in design and other factors can yield a meaningless summary result, but the evaluation of reasons for the heterogeneity among studies can be very insightful. It may be argued that these studies are of intrinsic interest on their own, even though it is not appropriate to produce a single summary estimate of effect.

Variation among k trials is usually assessed using Cochran's Q statistic, a chi-squared (χ 2 ) test of heterogeneity with k-1 degrees of freedom. This test has relatively poor power to detect heterogeneity among small numbers of trials; consequently, an α-level of 0.10 is used to test hypotheses 38 , 39 .

Heterogeneity of results among trials is better quantified using the inconsistency index I 2 , which describes the percentage of total variation across studies 40 . Uncertainty intervals for I 2 (dependent on Q and k) are calculated using the method described by Higgins and Thompson 41 . Negative values of I 2 are put equal to zero, consequently I 2 lies between 0 and 100%. A value >75% may be considered substantial heterogeneity 41 . This statistic is less influenced by the number of trials compared with other methods used to estimate the heterogeneity and provides a logical and readily interpretable metric but it still can be unstable when only a few studies are combined 42 .

Given that there are several potential sources of heterogeneity in the data, several steps should be considered in the investigation of the causes. Although random-effects models are appropriate, it may be still very desirable to examine the data to identify sources of heterogeneity and to take steps to produce models that have a lower level of heterogeneity, if appropriate. Further, if the studies examined are highly heterogeneous, it may be not appropriate to present an overall summary estimate, even when random effects models are used. As Petiti notes 43 , statistical analysis alone will not make contradictory studies agree; critically, however, one should use common sense in decision-making. Despite heterogeneity in responses, if all studies had a positive point direction and the pooled confidence interval did not include zero, it would not be logical to conclude that there was not a positive effect, provided that sufficient studies and subject numbers were present. The appropriateness of the point estimate of the effect is much more in question.

Some of the ways to investigate the reasons for heterogeneity; are subgroup analysis and meta-regression. The subgroup analysis approach, a variation on those described above, groups categories of subjects (e.g., by age, sex) to compare effect sizes. The meta-regression approach uses regression analysis to determine the influence of selected variables (the independent variables) on the effect size (the dependent variable). In a meta-regresregression, studies are regarded as if they were individual patients, but their effects are properly weighted to account for their different variances 44 .

Sensitivity analyses have also been used to examine the effects of studies identified as being aberrant concerning conduct or result, or being highly influential in the analysis. Recently, another method has been proposed that reduces the weight of studies that are outliers in meta-analyses 45 . All of these methods for examining heterogeneity have merit, and the variety of methods available reflects the importance of this activity.

Presentation of results

A useful graph, presented in the PRISMA statement 11 , is the four-phase flow diagram ( Figure 3 ).

This flow-diagram depicts the flow of information through the different phases of a systematic review or meta-analysis. It maps out the number of records identified, included and excluded, and the reasons for exclusions. The results of meta-analyses are often presented in a forest plot, where each study is shown with its effect size and the corresponding 95% confidence interval ( Figure 4 ).

The pooled effect and 95% confidence interval is shown in the bottom in the same line with "Overall". In the right panel of Figure 4 , the cumulative meta-analysis is graphically displayed, where data are entered successively, typically in the order of their chronological appearance 46 , 47 . Such cumulative meta-analysis can retrospectively identify the point in time when a treatment effect first reached conventional levels of significance. Cumulative meta-analysis is a compelling way to examine trends in the evolution of the summary-effect size, and to assess the impact of a specific study on the overall conclusions 46 . The figure shows that many studies were performed long after cumulative meta-analysis would have shown a significant beneficial effect of antibiotic prophylaxis in colon surgery.

Biases in meta-analysis

Although the intent of a meta-analysis is to find and assess all studies meeting the inclusion criteria, it is not always possible to obtain these. A critical concern is the papers that may have been missed. There is good reason to be concerned about this potential loss because studies with significant, positive results (positive studies) are more likely to be published and, in the case of interventions with a commercial value, to be promoted, than studies with non-significant or "negative" results (negative studies). Studies that produce a positive result, especially large studies, are more likely to have been published and, conversely, there has been a reluctance to publish small studies that have non-significant results. Further, publication bias is not solely the responsibility of editorial policy as there is reluctance among researchers to publish results that were either uninteresting or are not randomized 48 . There are, however, problems with simply including all studies that have failed to meet peer-review standards. All methods of retrospectively dealing with bias in studies are imperfect.

It is important to examine the results of each meta-analysis for evidence of publication bias. An estimation of likely size of the publication bias in the review and an approach to dealing with the bias is inherent to the conduct of many meta-analyses. Several methods have been developed to provide an assessment of publication bias; the most commonly used is the funnel plot. The funnel plot provides a graphical evaluation of the potential for bias and was developed by Light and Pillemer 49 and discussed in detail by Egger and colleagues 50 , 51 . A funnel plot is a scatterplot of treatment effect against a measure of study size. If publication bias is not present, the plot is expected to have a symmetric inverted funnel shape, as shown in Figure 5A .

In a study in which there is no publication bias, larger studies (i.e., have lower standard error) tend to cluster closely to the point estimate. As studies become less precise, such as in smaller trials (i.e., have a higher standard error), the results of the studies can be expected to be more variable and are scattered to both sides of the more precise larger studies. Figure 5A shows that the smaller, less precise studies are, indeed, scattered to both sides of the point estimate of effect and that these seem to be symmetrical, as an inverted funnel-plot, showing no evidence of publication bias. In contrast to Figure 5A , Figure 5B shows evidence of publication bias. There is evidence of the possibility that studies using smaller numbers of subjects and showing an decrease in effect size (lower odds ratio) were not published.

Asymmetry of funnel plots is not solely attributable to publication bias, but may also result from clinical heterogeneity among studies. Sources of clinical heterogeneity include differences in control or exposure of subjects to confounders or effect modifiers, or methodological heterogeneity between studies; for example, a failure to conceal treatment allocation. There are several statistical tests for detecting funnel plot asymmetry; for example, Eggers linear regression test 50 , and Begg's rank correlation test 52 but these do not have considerable power and are rarely used. However, the funnel plot is not without problems. If high precision studies really are different than low precision studies with respect to effect size (e.g., due different populations examined) a funnel plot may give a wrong impression of publication bias 53 . The appearance of the funnel plot plot can change quite dramatically depending on the scale on the y-axis - whether it is the inverse square error or the trial size 54 .

Other types of biases in meta-analysis include the time lag bias, selective reporting bias and the language bias. The time lag bias arises from the published studies, when those with striking results are published earlier than those with non-significant findings 55 . Moreover, it has been shown that positive studies with high early accrual of patients are published sooner than negative trials with low early accrual 56 . However, missing studies, either due to publication bias or time-lag bias may increasingly be identified from trials registries.

The selective reporting bias exists when published articles have incomplete or inadequate reporting. Empirical studies have shown that this bias is widespread and of considerable importance when published studies were compared with their study protocols 29 , 30 . Furthermore, recent evidence suggests that selective reporting might be an issue in safety outcomes and the reporting of harms in clinical trials is still suboptimal 57 . Therefore, it might not be possible to use quantitative objective evidence for harms in performing meta-analyses and making therapeutic decisions.

Excluding clinical trials reported in languages other than English from meta-analyses may introduce the language bias and reduce the precision of combined estimates of treatment effects. Trials with statistically significant results have been shown to be published in English 58 . In contrast, a later more extensive investigation showed that trials published in languages other than English tend to be of lower quality and produce more favourable treatment effects than trials published in English and concluded that excluding non-English language trials has generally only modest effects on summary treatment effect estimates but the effect is difficult to predict for individual meta-analyses 59 .

Evolution of meta-analyses

The classical meta-analysis compares two treatments while network meta-analysis (or multiple treatment metaanalysis) can provide estimates of treatment efficacy of multiple treatment regimens, even when direct comparisons are unavailable by indirect comparisons 60 . An example of a network analysis would be the following. An initial trial compares drug A to drug B. A different trial studying the same patient population compares drug B to drug C. Assume that drug A is found to be superior to drug B in the first trial. Assume drug B is found to be equivalent to drug C in a second trial. Network analysis then, allows one to potentially say statistically that drug A is also superior to drug C for this particular patient population. (Since drug A is better than drug B, and drug B is equivalent to drug C, then drug A is also better to drug C even though it was not directly tested against drug C.)

Meta-analysis can also be used to summarize the performance of diagnostic and prognostic tests. However, studies that evaluate the accuracy of tests have a unique design requiring different criteria to appropriately assess the quality of studies and the potential for bias. Additionally, each study reports a pair of related summary statistics (for example, sensitivity and specificity) rather than a single statistic (such as a risk ratio) and hence requires different statistical methods to pool the results of the studies 61 . Various techniques to summarize results from diagnostic and prognostic test results have been proposed 62 – 64 . Furthermore, there are many methodologies for advanced meta-analysis that have been developed to address specific concerns, such as multivariate meta-analysis 65 – 67 , and special types of meta-analysis in genetics 68 but will not be discussed here.

Meta-analysis is no longer a novelty in medicine. Numerous meta-analyses have been conducted for the same medical topic by different researchers. Recently, there is a trend to combine the results of different meta-analyses, known as a meta-epidemiological study, to assess the risk of bias 79 , 70 .

Conclusions

The traditional basis of medical practice has been changed by the use of randomized, blinded, multicenter clinical trials and meta-analysis, leading to the widely used term "evidence-based medicine". Leaders in initiating this change have been the Cochrane Collaboration who have produced guidelines for conducting systematic reviews and meta-analyses 10 and recently the PRISMA statement, a helpful resource to improve reporting of systematic reviews and meta-analyses has been released 11 . Moreover, standards by which to conduct and report meta-analyses of observational studies have been published to improve the quality of reporting 71 .

Meta-analysis of randomized clinical trials is not an infallible tool, however, and several examples exist of meta-analyses which were later contradicted by single large randomized controlled trials, and of meta-analyses addressing the same issue which have reached opposite conclusions 72 . A recent example, was the controversy between a meta-analysis of 42 studies 73 and the subsequent publication of the large-scale trial (RECORD trial) that did not support the cardiovascular risk of rosiglitazone 74 . However, the reason for this controversy was explained by the numerous methodological flaws found both in the meta-analysis and the large clinical trial 75 .

No single study, whether meta-analytic or not, will provide the definitive understanding of responses to treatment, diagnostic tests, or risk factors influencing disease. Despite this limitation, meta-analytic approaches have demonstrable benefits in addressing the limitations of study size, can include diverse populations, provide the opportunity to evaluate new hypotheses, and are more valuable than any single study contributing to the analysis. The conduct of the studies is critical to the value of a meta-analysis and the methods used need to be as rigorous as any other study conducted.

Diagnostic accuracy of artificial intelligence models in detecting osteoporosis using dental images: a systematic review and meta-analysis

• Published: 23 August 2024

Cite this article

• Gita Khadivi   ORCID: orcid.org/0000-0003-2949-0376 1 ,
• Abtin Akhtari   ORCID: orcid.org/0000-0001-9966-1383 2 ,
• Farshad Sharifi   ORCID: orcid.org/0000-0002-2035-6587 3 ,
• Nicolette Zargarian   ORCID: orcid.org/0009-0007-4012-1789 4 ,
• Saharnaz Esmaeili   ORCID: orcid.org/0000-0002-5187-3261 5 ,
• Mitra Ghazizadeh Ahsaie   ORCID: orcid.org/0000-0001-7028-748X 1 &
• Soheil Shahbazi   ORCID: orcid.org/0000-0002-1155-7459 6  

The current study aimed to systematically review the literature on the accuracy of artificial intelligence (AI) models for osteoporosis (OP) diagnosis using dental images. A thorough literature search was executed in October 2022 and updated in November 2023 across multiple databases, including PubMed, Scopus, Web of Science, and Google Scholar. The research targeted studies using AI models for OP diagnosis from dental radiographs. The main outcomes were the sensitivity and specificity of AI models regarding OP diagnosis. The “meta” package from the R Foundation was selected for statistical analysis. A random-effects model, along with 95% confidence intervals, was utilized to estimate pooled values. The Quality Assessment of Diagnostic Accuracy Studies (QUADAS-2) tool was employed for risk of bias and applicability assessment. Among 640 records, 22 studies were included in the qualitative analysis and 12 in the meta-analysis. The overall sensitivity for AI-assisted OP diagnosis was 0.85 (95% CI, 0.70–0.93), while the pooled specificity equaled 0.95 (95% CI, 0.91–0.97). Conventional algorithms led to a pooled sensitivity of 0.82 (95% CI, 0.57–0.94) and a pooled specificity of 0.96 (95% CI, 0.93–0.97). Deep convolutional neural networks exhibited a pooled sensitivity of 0.87 (95% CI, 0.68–0.95) and a pooled specificity of 0.92 (95% CI, 0.83–0.96). This systematic review corroborates the accuracy of AI in OP diagnosis using dental images. Future research should expand sample sizes in test and training datasets and standardize imaging techniques to establish the reliability of AI-assisted methods in OP diagnosis through dental images.

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Department of Oral and Maxillofacial Radiology, School of Dentistry, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Gita Khadivi & Mitra Ghazizadeh Ahsaie

School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Abtin Akhtari

Elderly Health Research Center, Endocrinology and Metabolism Population Sciences Institute, Tehran University of Medical Sciences, Tehran, Iran

Farshad Sharifi

School of Dentistry, Research Institute for Dental Sciences, Mkhitar Heratsi Yerevan State Medical University, Yerevan, Armenia

Nicolette Zargarian

Dentofacial Deformities Research Center, Research Institute of Dental Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Saharnaz Esmaeili

Dental Research Center, Research Institute for Dental Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

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Khadivi, G., Akhtari, A., Sharifi, F. et al. Diagnostic accuracy of artificial intelligence models in detecting osteoporosis using dental images: a systematic review and meta-analysis. Osteoporos Int (2024). https://doi.org/10.1007/s00198-024-07229-8

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DOI : https://doi.org/10.1007/s00198-024-07229-8

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