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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.

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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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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Department of Ecology and Evolution, Stony Brook University, Stony Brook, 11794-5245, New York, USA

Jessica Gurevitch

School of Biological Sciences, Royal Holloway University of London, Egham, TW20 0EX, Surrey, UK

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

Gavin Stewart

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All authors contributed equally in designing the study and writing the manuscript, and so are listed alphabetically.

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Correspondence to Jessica Gurevitch , Julia Koricheva , Shinichi Nakagawa or Gavin Stewart .

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Reviewer Information Nature thanks D. Altman, M. Lajeunesse, D. Moher and G. Romero for their contribution to the peer review of this work.

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Gurevitch, J., Koricheva, J., Nakagawa, S. et al. Meta-analysis and the science of research synthesis. Nature 555 , 175–182 (2018). https://doi.org/10.1038/nature25753

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A Guide to Conducting a Meta-Analysis

Affiliations.

1 Department of Psychology, Faculty of Arts and Social Sciences, National University of Singapore, Block AS4, Level 2, 9 Arts Link, Singapore, 117570, Singapore. [email protected].
2 Department of Psychology, Faculty of Arts and Social Sciences, National University of Singapore, Block AS4, Level 2, 9 Arts Link, Singapore, 117570, Singapore.
PMID: 27209412
DOI: 10.1007/s11065-016-9319-z

Meta-analysis is widely accepted as the preferred method to synthesize research findings in various disciplines. This paper provides an introduction to when and how to conduct a meta-analysis. Several practical questions, such as advantages of meta-analysis over conventional narrative review and the number of studies required for a meta-analysis, are addressed. Common meta-analytic models are then introduced. An artificial dataset is used to illustrate how a meta-analysis is conducted in several software packages. The paper concludes with some common pitfalls of meta-analysis and their solutions. The primary goal of this paper is to provide a summary background to readers who would like to conduct their first meta-analytic study.

Keywords: Literature review; Meta-analysis; Moderator analysis; Systematic review.

Publication types

Research Support, Non-U.S. Gov't
Data Interpretation, Statistical
Meta-Analysis as Topic*
Publication Bias
Review Literature as Topic

Systematic Reviews and Meta Analysis

Getting Started
Guides and Standards
Review Protocols
Databases and Sources
Randomized Controlled Trials
Controlled Clinical Trials
Observational Designs
Tests of Diagnostic Accuracy
Software and Tools
Where do I get all those articles?
Collaborations
EPI 233/528
Countway Mediated Search
Risk of Bias (RoB)

Systematic review Q & A

What is a systematic review.

A systematic review is guided filtering and synthesis of all available evidence addressing a specific, focused research question, generally about a specific intervention or exposure. The use of standardized, systematic methods and pre-selected eligibility criteria reduce the risk of bias in identifying, selecting and analyzing relevant studies. A well-designed systematic review includes clear objectives, pre-selected criteria for identifying eligible studies, an explicit methodology, a thorough and reproducible search of the literature, an assessment of the validity or risk of bias of each included study, and a systematic synthesis, analysis and presentation of the findings of the included studies. A systematic review may include a meta-analysis.

For details about carrying out systematic reviews, see the Guides and Standards section of this guide.

Is my research topic appropriate for systematic review methods?

A systematic review is best deployed to test a specific hypothesis about a healthcare or public health intervention or exposure. By focusing on a single intervention or a few specific interventions for a particular condition, the investigator can ensure a manageable results set. Moreover, examining a single or small set of related interventions, exposures, or outcomes, will simplify the assessment of studies and the synthesis of the findings.

Systematic reviews are poor tools for hypothesis generation: for instance, to determine what interventions have been used to increase the awareness and acceptability of a vaccine or to investigate the ways that predictive analytics have been used in health care management. In the first case, we don't know what interventions to search for and so have to screen all the articles about awareness and acceptability. In the second, there is no agreed on set of methods that make up predictive analytics, and health care management is far too broad. The search will necessarily be incomplete, vague and very large all at the same time. In most cases, reviews without clearly and exactly specified populations, interventions, exposures, and outcomes will produce results sets that quickly outstrip the resources of a small team and offer no consistent way to assess and synthesize findings from the studies that are identified.

If not a systematic review, then what?

You might consider performing a scoping review . This framework allows iterative searching over a reduced number of data sources and no requirement to assess individual studies for risk of bias. The framework includes built-in mechanisms to adjust the analysis as the work progresses and more is learned about the topic. A scoping review won't help you limit the number of records you'll need to screen (broad questions lead to large results sets) but may give you means of dealing with a large set of results.

This tool can help you decide what kind of review is right for your question.

Can my student complete a systematic review during her summer project?

Probably not. Systematic reviews are a lot of work. Including creating the protocol, building and running a quality search, collecting all the papers, evaluating the studies that meet the inclusion criteria and extracting and analyzing the summary data, a well done review can require dozens to hundreds of hours of work that can span several months. Moreover, a systematic review requires subject expertise, statistical support and a librarian to help design and run the search. Be aware that librarians sometimes have queues for their search time. It may take several weeks to complete and run a search. Moreover, all guidelines for carrying out systematic reviews recommend that at least two subject experts screen the studies identified in the search. The first round of screening can consume 1 hour per screener for every 100-200 records. A systematic review is a labor-intensive team effort.

How can I know if my topic has been been reviewed already?

Before starting out on a systematic review, check to see if someone has done it already. In PubMed you can use the systematic review subset to limit to a broad group of papers that is enriched for systematic reviews. You can invoke the subset by selecting if from the Article Types filters to the left of your PubMed results, or you can append AND systematic[sb] to your search. For example:

"neoadjuvant chemotherapy" AND systematic[sb]

The systematic review subset is very noisy, however. To quickly focus on systematic reviews (knowing that you may be missing some), simply search for the word systematic in the title:

"neoadjuvant chemotherapy" AND systematic[ti]

Any PRISMA-compliant systematic review will be captured by this method since including the words "systematic review" in the title is a requirement of the PRISMA checklist. Cochrane systematic reviews do not include 'systematic' in the title, however. It's worth checking the Cochrane Database of Systematic Reviews independently.

You can also search for protocols that will indicate that another group has set out on a similar project. Many investigators will register their protocols in PROSPERO , a registry of review protocols. Other published protocols as well as Cochrane Review protocols appear in the Cochrane Methodology Register, a part of the Cochrane Library .

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Study Design 101: Meta-Analysis

Case Report
Case Control Study
Cohort Study
Randomized Controlled Trial
Practice Guideline
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.

Evidence Pyramid - Navigation

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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.

Person analyzing results of meta-analysis

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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How to do a Meta Analysis: Methodology, Pros & Cons

Have you been searching for a method where you can collate all your research findings and analyze them statistically? If yes, have you considered meta-analysis? If not, grab a seat as we go through the concept of meta-analysis, what it can be used for, and how you can use it to improve how you collect data as a researcher/investigator.

Alright, to begin with, what is a meta-analysis?

What is a meta-analysis?

Meta-analysis is a method primarily used to determine the prevalence of truth or the common differences in research with similar research questions . It puts together the results from different scientific researches and analyzes them using statistical methods.

The term meta-analysis was first mentioned and clearly used in the 1970s. This happened when a statistician known as Gene Glass used the word as he made a call for statisticians to find more improved ways to conclude their field research findings.

For over a century or more now, researchers have been collecting data from numerous studies regardless of the call for improved data collection techniques . One of these cases is that of immunity and mortality in soldiers of 1904. While searching for averages in the results that may provide insight on the effects of the typhoid vaccine being administered to the soldiers, all the results from the findings were mixed up.

This incident and many others are why Gene Glass demanded better data recording techniques from all statisticians.

Purpose of meta-analysis in research

It is unarguable the volume of new studies that are being published by researchers. One thing meta-analysis does is review all these studies and narrow them down.

The purpose of meta-analysis is that it seeks to determine whether an effect is present in a study and also determine whether the present effect is a positive one or a negative one. Meta-analysis examines the strengths of the results of a study. It checks whether there is substantial evidence to back up the findings of a study.

Another aim of meta-analysis is that it analyzes all the results of previously published theses on a subject. This is to detect if a common trend in all the studies. When a researcher establishes a trend among many studies it has higher statistical significance than when the study is conducted alone. This is because the validity of research is increased significantly when there are visible differences.

Meta-analysis can be used in fields such as medical research, psychology, and other studies.

Read: Systematic Errors in Research: Definition, Examples

Why Meta-Analysis?

Meta-analysis is designed to review the information and put it into simpler terms. Meta-analysis however follows some principles which are:

Meta-analysis must be done systematically
The basis of meta-analysis is quantitative analysis.
There must be a number of results for meta-analysis to occur.

The reassessment carried out by meta-analysis provides trends that improve decisions and subsequent research and this is why these reviews

Hence, the reason why meta-analysis is helpful in research are as follows:

1. In research, meta-analysis evaluates effects in diverse participants that are in subsets of a study subgroup.

2. Meta-analysis establishes another hypothesis that can set precedence for future studies.

3. Applying meta-analysis in your study can prove statistical significance.

4. A meta-analysis helps to overcome the issue of a small sample size in research since it tests the outcome of various studies across similar subjects or topics.

Read: Margin of error – Definition, Formula + Application

How to conduct a meta-analysis

1. Select your topic : The first thing to do before conducting a meta-analysis review is to choose the topic you want the meta-analysis to be focused on. You can develop your research questions using the PICO model which stands for Population Intervention Comparison and Outcome.

For example, are women at a higher risk of cervical cancer if they used oral contraceptives in 10 years or more than women who never used oral contraceptives? This research hypothesis would help the researcher to identify the population for the study and also cervical cancer can be identified as the result of long-term use of contraceptives.

To avoid duplication of research, you should confirm that there has never been published research on the same topic as yours.

2. Review the guidelines for conducting a meta-analysis : there are many guidelines available to help a researcher when conducting a meta-analysis review. Have them by your side and follow the instructions step by step.

3. Establish your standards : Before commencing your meta-analysis review, determine your research criteria such as your sample size, the type of study you want it to be, and even the language you want to publicize the journal in. Define the variables that will be obtained from your research clearly.

4. Apply for systematic review : make use of systematic review to detect your primary data in your database. This will help to reduce the probability of not finding out about all the published articles that are the same as your topic.

You can also request unavailable data or missing data from the authors of the published articles.

5. Plan your questions : Ensure you use the most efficient statistical model to plan your research questions. Once you are done planning your question, run your meta-analysis test.

6. Record and Report : Once your meta-analysis test results are available, record your research findings carefully and report your findings. Make sure your reports are transparent and replicable. Also, provide sufficient data or information about your just-concluded study. Let your report also include the software, the standard, and the method used to carry out the research.

7. Draw your conclusion : the last part is drawing a conclusion as the researcher that is bias-free and represents the accurate outcome of the study. Enumerate your research findings and explain how they can be generalized to the population.

Meta-analysis methodologies

Step One: The first step is to develop the objective of the research in the form of a hypothesis or questions. This should be done before conducting day research to reduce the risk of insignificant variables appearing in the study.

Step Two : The second step is to take precautions concerning the objective developed for the test. This means that secondary or supporting objectives should be formulated to back up the primary objectives. This is in case the primary objectives do not cover the complete study.

The purpose of the meta-analysis methodology is to set primary and secondary objectives in advance for the research to be carried out.

Read: Survey Errors To Avoid: Types, Sources, Examples, Mitigation

Systematic review vs Meta-Analysis

The systematic review is a rigorous method of research but not as rigorous as compared to meta-analysis. This is because a systematic review focuses on analyzing only one research question.

For example, a researcher conducts a study about contraceptives and cervical cancer. The systematic review will only focus on the association between using oral contraceptives for the long term and having cervical cancer.

Systematic reviews are therefore used to reduce research bias.

Because meta-analysis is quantitative and more rigorous than a systematic review, it will not only provide the researcher with an overview of the subject, it also provides a quantitative analysis of whether a treatment performs better.

The meta-analysis also takes it a step further to provide a prediction or probability of the likelihood of a person developing an illness or disease if the person shows some characteristics.

It is noteworthy that meta-analysis is a subset of systematic review; however, meta-analysis is not always present in a systematic review.

Because systematic review focuses on one specific relationship, a researcher is able to draw conclusions and make reliable decisions from the findings of the study.

A meta-analysis, on the other hand, analyses multiple outcomes from different studies which, if a researcher is not careful, may draw a biased conclusion.

Advantages of meta-analysis

Here are the advantages of using meta-analysis in a study.

Meta-analysis gives a study better statistical power and this, in turn, allows generalization of the result to the entire population.
Meta-analysis provides accurate evidence as a result of analyzing different studies trends.
Meta-analyses are used by researchers to review large and sometimes complex research.
In a meta-analysis, the tested hypothesis and the results are essential because meta-analysis is a delicate method.
Meta-Analysis has the ability to be totally objective in analyzing and evaluating research outcomes.

From the points listed above, you can see that the advantages of the meta-analysis are the qualitative reviews obtained from a large sample which in most cases is also complex. Also because meta-analysis is sensitive in research the results and the hypothesis that is studied are very important.

Read: Type I vs Type II Errors: Definition, Examples & Prevention

Disadvantages and limitations of meta-analysis

A meta-analysis is indeed a powerful tool in research, however, it has some disadvantages. Some of its disadvantages are:

Meta-analysis is time-consuming. This is because it reviews outcomes from diverse studies.
To perform meta-analysis in a research complex statistical techniques and relevant skills and needed.
Because of the complex techniques needed to perform a meta-analysis, it is difficult to conduct.
Meta-analysis is not useful in all research. This means that a researcher cannot perform meta-analysis in all research.
If meta-analysis cannot detect most existing research on a subject, it can lead the researcher to draw wrong conclusions.

FAQs about meta-analysis

How do I know if I can do a meta-analysis?

If your studies seek to address the same results, they are measured or reviewed using the same method and the same analysis approach but still produce different results, then you should consider introducing a meta-analysis review.

If these studies provide you with sufficient information to estimate and understand the effects on the size of interest, then it may be possible to use meta-analysis.

So as a researcher or investigator, you can be sure to use a meta-analysis review if your study has similar topics or subjects, similar treatments, similar interventions, and similar results.

You should also be careful to take a wider perspective into consideration while applying meta-analysis as it is often appropriate than applying meta-analysis to just one clinical research or study.

When should a meta-analysis not be used?

In some cases, meta-analysis can be a hindrance rather than being helpful.

1. Meta-analysis should not suffice if the research is a combination of diverse studies. For example combining pineapples with grapes.

If there are no similarities in the subjects of study meta-analysis is best avoided because the study may lose its meaning.

Combining topics that should be conducted separately or extremely different results of studies in a single meta-analysis review, should not be encouraged.

2. Conducting a meta-analysis study on already published results that has high biases may lead the researcher to an erroneous conclusion. This is because if there are biases in some of the individual research, meta-analysis will combine the errors and give incorrect results which the researcher may take credible.

3. When confronted with serious reporting and publication biases meta-analysis we most likely produce an inaccurate conclusion.

Read: Research Bias: Definition, Types + Examples

In these three instances, it is best to not use meta-analysis to review your studies. Be quick to shield your research from the high risk of biases and time and resources wastage that can be frustrating.

Analyze your data and your research objectives, understand what the most appropriate review method for your data is before conducting any study.

What is a good sample size for a meta-analysis?

Meta-analysis is best conducted when the sample size is small. To understand what a good sample size is for meta-analysis, a researcher must know that it is best to keep the sample size small if it meets the researcher’s outlined requirements.

This is to say that the criteria developed by the researcher for the study determine the sample size be adopted.

Conducting meta-analysis with sample size is not only easy but it produces rather interesting results than a large sample size. In reality, studies with significant and interesting results have a higher chance of getting published.

Meta-analysis is helpful if your studies are based on finding the similarity in the Trent between existing research and the new one. However, be mindful of the studies you combine so that your research will not be at risk of biases which can lead to erroneous conclusions.

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Open access
Published: 14 November 2023

Employment of patients with rheumatoid arthritis - a systematic review and meta-analysis

Lilli Kirkeskov 1 , 2 &
Katerina Bray 1 , 3

BMC Rheumatology volume 7 , Article number: 41 ( 2023 ) Cite this article

1678 Accesses

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Patients with rheumatoid arthritis (RA) have difficulties maintaining employment due to the impact of the disease on their work ability. This review aims to investigate the employment rates at different stages of disease and to identify predictors of employment among individuals with RA.

The study was carried out according to the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines focusing on studies reporting employment rate in adults with diagnosed RA. The literature review included cross-sectional and cohort studies published in the English language between January 1966 and January 2023 in the PubMed, Embase and Cochrane Library databases. Data encompassing employment rates, study demographics (age, gender, educational level), disease-related parameters (disease activity, disease duration, treatment), occupational factors, and comorbidities were extracted. Quality assessment was performed employing Newcastle–Ottawa Scale. Meta-analysis was conducted to ascertain predictors for employment with odds ratios and confidence intervals, and test for heterogeneity, using chi-square and I 2 -statistics were calculated. This review was registered with PROSPERO (CRD42020189057).

Ninety-one studies, comprising of a total of 101,831 participants, were included in the analyses. The mean age of participants was 51 years and 75.9% were women. Disease duration varied between less than one year to more than 18 years on average. Employment rates were 78.8% (weighted mean, range 45.4–100) at disease onset; 47.0% (range 18.5–100) at study entry, and 40.0% (range 4–88.2) at follow-up. Employment rates showed limited variations across continents and over time. Predictors for sustained employment included younger age, male gender, higher education, low disease activity, shorter disease duration, absence of medical treatment, and the absence of comorbidities.

Notably, only some of the studies in this review met the requirements for high quality studies. Both older and newer studies had methodological deficiencies in the study design, analysis, and results reporting.

Conclusions

The findings in this review highlight the prevalence of low employment rates among patients with RA, which increases with prolonged disease duration and higher disease activity. A comprehensive approach combining clinical and social interventions is imperative, particularly in early stages of the disease, to facilitate sustained employment among this patient cohort.

Peer Review reports

Rheumatoid arthritis (RA) is a chronic, inflammatory joint disease that can lead to joint destruction. RA particularly attacks peripheral joints and joint tissue, gradually resulting in bone erosion, destruction of cartilage, and, ultimately, loss of joint integrity. The prevalence of RA varies globally, ranging from 0.1- 2.0% of the population worldwide [ 1 , 2 ]. RA significantly reduces functional capacity, quality of life, and results in an increase in sick leave, unemployment, and early retirement [ 3 , 4 , 5 ]. The loss of productivity due to RA is substantial [ 2 , 5 , 6 , 7 ]. A 2015 American study estimated the cost of over $250 million annually from RA-related absenteeism in United States alone [ 8 ].

Research has highlighted the importance of maintaining a connection to the labour market [ 3 , 9 ], Even a short cessation from work entails a pronounced risk of enduring work exclusion [ 10 ]. In Denmark merely 55% on sick leave for 13 weeks succeeded in re-joining the workforce within one year. Among those on sick leave for 26 weeks, only 40% returned to work within the same timeframe [ 11 ]. Sustained employment is associated with an improved health-related quality of life [ 12 , 13 ]. Early and aggressive treatment of RA is crucial for importance in achieving remission and a favourable prognosis reducing the impact of the disease [ 2 , 14 , 15 , 16 ]. Therefore, initiating treatment in a timely manner and supporting patients with RA in maintaining their jobs with inclusive and flexible workplaces if needed is critical [ 3 , 17 ].

International studies have indicated, that many patients with RA are not employed [ 18 ]. In 2020, the average employment rate across Organization for Economic Co-operation and Development (OECD) countries was 69% in the general population (15 to 64 years of age), exhibiting variations among countries, ranging from 46–47% in South Africa and India to 85% in Iceland [ 19 ]. Employment rates were lower for individuals with educational levels below upper secondary level compared to those with upper secondary level or higher education [ 19 ]. For individuals suffering with chronic diseases, the employment rates tend to be lower. Prognostic determinants for employment in the context of other chronic diseases encompasses the disease’s severity, employment status prior to getting a chronic disease, and baseline educational level [ 20 , 21 , 22 ]. These somatic and social factors may similarly influence employment status of patients with RA. Several factors, including the type of job (especially physically demanding occupations), support from employers and co-workers, social safety net, and disease factors such as duration and severity, could have an impact on whether patients with RA are employed [ 17 , 23 , 24 ]. Over the years, politicians and social welfare systems have tried to improve the employment rates for patients with chronic diseases. In some countries, rehabilitation clinics have been instrumental in supporting patients to remain in paid work. Healthcare professionals who care for patients with RA occupy a pivotal role in preventing work-related disability and support the patients to remain in work. Consequently, knowledge of the factors that contribute to retention of patients with RA at work is imperative [ 17 , 25 ].

The aim of this study is therefore to conduct a systematic review, with a primary focus on examining employment rates among patients with RA at the onset of the disease, at study entry, and throughout follow-up. Additionally, this study intends to identify predictors of employment. The predefined predictors, informed by the author’s comprehensive understanding of the field and specific to RA, encompass socioeconomic factors such as age, gender, level of education, employment status prior to the disease, disease stage and duration, treatment modalities, and comorbidities, including depression, which are relevant both to RA and other chronic conditions [ 26 ].

This systematic review was carried out according to Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) for studies that included employment rate in patients with rheumatoid arthritis [ 27 ]. PROSPERO registration number: CRD42020189057.

Selection criteria and search strategies

A comprehensive literature search was conducted, covering the period from January 1966 to January 2023 across the PubMed, Embase, and Cochrane Library databases using the following search terms: (Rheumatoid arthritis OR RA) AND (employment OR return to work). Only studies featuring a minimum cohort size of thirty patients and articles in the English language were deemed eligible for inclusion.

The initial screening of articles was based on the titles and abstracts. Studies comprising a working-age population, with current or former employment status, and with no limitations to gender, demographics, or ethnicity were included in this review. Articles addressing topics of employment, work ability or disability, return to work or disability pension were encompassed within the scope of this review. Full-time and part-time employment, but not ‘working as housewives’ was included in this review’s definition of employment. Studies involving other inflammatory diseases than RA were excluded. Reference lists in the selected articles were reviewed, and more articles were included if relevant. A review of the reference lists in the initially selected articles was conducted, with additional articles incorporated if they proved relevant to the research objectives. The eligible study designs encompassed cohort studies, case–control studies, and cross-sectional studies. All other study designs, including reviews, case series/case reports, in vitro studies, qualitative studies, and studies based on health economics were systematically excluded from the review.

Data extraction, quality assessment and risk-of-bias

The data extraction from the selected articles included author names, year of publication, study design, date for data collection, employment rate, study population, age, gender, educational level, ethnicity, disease duration, and pharmacological treatment. To ensure comprehensive evaluation of study quality and potential bias, quality assessment was independently assessed by two reviewers (LK and KB) using the Newcastle–Ottawa Scale (NOS) for cross-sectional and cohort studies [ 28 ]. Any disparities in the assessment were resolved by discussion until consensus was reached. For cross-sectional studies the quality assessment included: 1) Selection (maximum 5 points): representativeness of the sample, sample size, non-respondents, ascertainment of the risk factor; 2) Comparability (maximum 2 points); study controls for the most important, and any additional factor; 3) Outcome (maximum 3 points): assessment of outcome, and statistical testing. For cohort studies the assessment included: 1) Selection (maximum 4 points): representativeness of the exposed cohort, selection of the non-exposed cohort, ascertainment of exposure, demonstration that the outcome of interest was not present at start of study; 2) Comparability (maximum 2 points): comparability of cohorts on the basis of the design or analysis; 3) Outcome (maximum 3 points): assessment of outcome, was the follow-up long enough for outcomes to occur, and adequacy of follow up of cohorts. The rating scale was based on 9–10 items dividing the studies into high (7–9/10), moderate (4–6) or low (0–3) quality. A low NOS score (range 0–3) indicated a high risk of bias, and a high NOS score (range 7–9/10) indicated a lower risk of bias.

Analytical approach

For outcomes reported in numerical values or percentages, the odds ratio along with their 95% confidence intervals (CI) were calculated, whenever feasible. Weighted means were calculated, and comparisons between these were conducted using t-test for unpaired data. Furthermore, meta-analysis concerning the pre-determined and potentially pivotal predictors for employment status, both at disease onset, study entry, and follow-up was undertaken. The predictors included age, gender, ethnicity, level of education, duration of disease, treatment, and the presence of comorbities, contingent upon the availability of the adequate data. Additionally, attempts have been made to find information regarding on job categorizations, disease activity (quantified through DAS28; disease activity score for number of swollen joints), and quality of life (SF-36 scores ranging from 0 (worst) to 100 (best)). Age was defined as (< = 50/ > 50 years), gender (male/female), educational level college education or more/no college education), race (Caucasian/not Caucasian), job type (non-manual/manual), comorbidities (not present/present), MTX ever (no/yes), biological treatment ever (no/yes), prednisolone ever (no/yes), disease duration, HAQ score (from 0–3)), joint pain (VAS from 1–10), and DAS28 score. Age, disease duration, HAQ score, VAS score, SF36 and DAS28 were in the studies reported by mean values and standard deviations (SD). Challenges were encountered during attempts to find data which could be used for analysing predictors of employment status before disease onset, and at follow-up, as well as factors related to treatments beyond MTX, prednisolone, and biological as predictors for being employed after disease onset. Test for heterogeneity was done using Chi-squared statistics and I 2 , where I 2 below 40% might not be important; 30–60% may represent moderate heterogeneity; 50–90% substantial heterogeneity; and 75–100% considerable heterogeneity. Meta-analysis for predictors for employment and odds ratio; confidence intervals; and test for heterogeneity were calculated using the software Review Manager (RevMan, version 5.3. Copenhagen: The Nordic Cochrane Centre, The Cochrane Collaboration, 2014).

General description of included studies

The search yielded a total of 2277 references addressing RA its association with employment. Following the initial title screen, 199 studies were considered relevant for further evaluation. Of those, 91 studies ultimately met the inclusion criteria. Figure 1 shows the results of the systematic search strategy.

Flow chart illustrating the systematic search for studies examining employment outcome in patients with rheumatoid arthritis

Table 1 summarizes the general characteristics of the included studies. The publication year of the included studies ranged from 1971 to 2022. Among the studies, 60 (66%) adopted a cross-sectional research design [ 13 , 18 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 129 ] with a total of 41,857 participants analysing data at a specific point in time. Concurrently, 31 studies (34%) adopted a cohort design [ 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 , 119 , 120 , 121 , 122 , 130 ] with a total of 59,974 participants. Most of these studies exhibited a small to moderate sample size, with a median of 652 participants. Additionally, single centre studies and studies from high-income countries were predominant. Study details are shown in Table 1 .

General description of study participants

On average, patients with RA were 51 years old, with an age range spanning from 42 to 64 years. Furthermore, the female population accounted for 75.9% of the patient cohort, with a range from 41 to 92%. The duration of the disease at study entry exhibited significant variability, ranging from less than one year up to more than 18 years on average.

Employment rate

At disease onset, the employment rate was 78.8% (weighted mean, range 45.4–100), at study entry 47.0% (range 18.5–100), and during the follow-up period 40.0% (range 4–88.2), as shown in Table 2 . Notably, a comparative analysis of the employment rates between Europe and North America indicated no substantial difference ( p = 0.93). However, the comparison between Europe, North America and ‘other continents’ did yield significant differences (or nearly differences) with p -values of 0.003 and 0.08, respectively.

The employment rate exhibited no change, when comparing studies from the 1980s through to 2022. Specifically, the weighted mean for the years 1981–2000 was 49.2%, aligning closely with the corresponding figures for the years 2001–2010 (49.2%) and 2011–2022 43.6%. These findings were statistically non-significant, with p -values of 0.80 for comparison between year 1981–2000 and 2001–2010; 0.66 for 2001–2010 and 2011–2022, and 0.94 for 1981–2000 and 2011–2022, shown in Figure S 1 , see Additional file.

Among the studies included in the analysis, nineteen studies included data of employment at follow-up, with durations ranging from 1 to 20 years, Table 2 . For instance, Jäntti, 1999 [ 97 ] reported an employment rate 69% one year after disease onset, which gradually declined to 50% after 15 years and further to 20% after 20 years. Similarly, Mäkisara, 1982 [ 63 ] demonstrated that 60% of the patients were employed 5 years after disease onset, 50% after 10 years, and 33% after 15 years. Nikiphorou, 2012 [ 101 ] reported an employment rate of 67% at study entry, which decreased to 43% after 10 years.

In addition, seven studies included data of employment rate among patients comparing different medical treatments [ 18 , 44 , 56 , 91 , 105 , 110 , 119 ]. These studies indicated that, on average, 55.0% (weighted mean) of the patients were employed after receiving treatment with MTX, while 42.8% after undergoing treatment with a combination of MTX + Adalimumab (all patients were employed at disease onset in these specific studies).

Predictors for employment

Information of normative comparison data to use for meta-analysis of predictors for employment at study entry was available for age, gender, educational level, race, job type, comorbidities, MTX at any time, biological treatment at any time, prednisolone at any time, disease duration, HAQ score, joint pain (VAS-score), and disease activity (DAS28 score). Predictors for employment at study entry was being younger /age below 50 years, being a male, higher educational level (college or more), non-manual work, having no comorbidities, no medical treatment, short disease duration, and low HAQ score, VAS-score, or DAS28 score. Heterogeneity was small for age, gender, medical treatment, and moderate for educational level, and job type as indicted by the I 2 values, Table 3 , and shown in detail in Figures S 2 , S 3 , S 4 , S 5 , S 6 , S 7 , S 8 , S 9 , S 10 , S 11 , S 12 , S 13 , S 14 , S 15 and S 16 , see Additional file.

Assessment of quality of included studies

All studies were subject to rigorous quality assessment. These assessments resulted in categorisation of either medium quality ( n = 64; 70%) or high-quality studies ( n = 27; 30%), with no studies falling into the low-quality category. The quality assessment is shown in Tables 4 and 5 .

Notably, many studies were characterised by several common attributes, including cross-sectional study design, single-centre-settings, relatively small sample sizes, and the reliance on self-reported patient data. When including only the high-quality studies in the analyses, the employment rates at study entry changed from 47% (weighted mean, all studies) to 50% (weighted mean, high quality studies).

Key findings

This systematic review has identified a decline in the employment rate among patients with RA, with a notable decrease from disease onset during the study entry to follow-up, where only half of the patients were employed. These findings corroborate earlier research that indicated a substantial decline in employment rates among patients with RA over time. Notably, previous studies have reported that approximately one third of patients with RA stopped working within 2 to 3 years after disease onset, and more than half was unable to work after 10 to 15 years [ 23 , 63 , 93 , 97 , 101 ]. Only few studies have included data from the general population, comparing the employment rates with the rates for patients with RA [ 89 , 90 ]. Comparisons with the general population further underscored the challenges faced by RA patients, as their employment rates were consistently lower.

Despite changes in medical treatment, social security systems, and societal norms over the past decades, there was no significant improvement in the employment for patients with RA. This pattern aligns with data from the Global Burden of Disease studies, highlighting the persistent need for novel approaches and dedicated efforts to support patients with RA in sustaining employment [ 2 , 123 ]. Recent recommendations from EULAR (European Alliance of Associations for Rheumatology) and ACR (American College of Rheumatology) have emphasized the importance of enabling individuals with rheumatic and musculoskeletal diseases to engage in healthy and sustainable work [ 17 , 124 , 125 ].

While different countries possess different social laws and health care systems for supporting patients with chronic diseases, the variations in the weighted mean of employment rates across countries were relatively minor.

In the meta-analysis, one of the strongest predictors for maintaining employment was younger age at disease onset [ 43 , 51 , 101 , 116 ]. Verstappen, 2004 found that older patients with RA had an increased risk of becoming work disabled, potentially caused by the cumulative effects of long-standing RA, joint damage, and diminished coping mechanisms, compared to younger patients [ 23 ].

More women than men develop RA, however this study showed that a higher proportion of men managed to remain employed compared to women [ 18 , 36 , 42 , 43 , 46 , 62 , 71 , 89 , 101 , 116 ]. Previous studies have shown inconsistent results in this regard. Eberhart, 2007 found that a significantly higher number of men with RA worked even though there was no difference in any disease state between the sexes [ 93 ]. De Roos,1999 showed that work-disabled women were less likely to be well-educated and more likely to be in a nonprofessional occupation than working women. Interestingly, there was no association of these variables among men. Type of work and disease activity may influence work capacity more in women than in men [ 46 ]. Sokka, 2010 demonstrated a lower DAS28 and HAQ-score in men compared to women among the still working patients with RA, which indicated that women continued working at higher disability and disease activity levels compared with men [ 18 ].

Disease duration also played a significant role as a predictor of employment outcomes [ 33 , 36 , 45 , 71 , 77 , 86 , 102 , 111 ]. Longer disease duration correlate with decreased employment likelihood, which could be attributed to older age and increased joint damage and disability in patients with longer-standing RA.

Higher educational levels were associated with a greater possibility of employment [ 30 , 43 , 45 , 46 , 51 , 62 , 86 ]. This is probably due to enhanced job opportunities, flexibility, lower physical workload, better insurance coverage, and improved health care for well-educated individuals. This is further supported by the fact that having a manual work was a predictor for not being employed [ 30 , 39 , 43 , 44 , 45 ].

Furthermore, health-related quality of life, as measured by SF 36, lower disease activity (DAS28 scores), reduced joint pain (VAS-score), and lower disability (HAQ score) were additionally predictors for being employed [ 33 , 35 , 36 , 45 , 71 , 86 ]. This support the statement that the fewer symptoms from RA, the greater the possibility of being able to work.

The results showed that the presence of comorbidity was a predictor for not being employed, aligning with findings from previous studies that chronic diseases such as cardiovascular disease, lung disease, diabetes, cancer, and depression reduced the chances of being employed [ 126 ]. Moreover, the risk of exiting paid work increased with multimorbidity [ 127 ].

While limited data were available for assessing the impact of treatment on employment, indications suggested that patients with RA were receiving medical treatments, such as MTX or biological medicine, were more likely to be unemployed. One possible explanation for this phenomenon could be that patients with RA, who were receiving medical treatment, had a more severe and a longer duration of RA compared to those, who had never been on medical treatment. However, the scarcity of relevant studies necessitates caution when drawing definitive conclusions in this regard.

Therefore, the predictors for employment found in this review were being younger, being a male, having higher education, low disease activity, low disease duration, and being without comorbidities. This is supported by previous studies [ 93 , 116 ]

In summary, this review underscores the importance of managing disease activity, offering early support to patients upon diagnosis, and reducing physically demanding work to maintain employment among patients with RA. Achieving success in this endeavour requires close cooperation among healthcare professionals, rehabilitation institutions, companies, and employers. Furthermore, it is important that these efforts are underpinned by robust social policies that ensure favourable working conditions and provide financial support for individuals with physical disabilities, enabling them to remain active in the labour market.

Strengths and limitations

The strength of this review and meta-analysis lies in the inclusion of a large number of articles originating from various countries. Furthermore, the data showed a consistent employment rate in high quality studies compared to all studies. However, there are some limitations to this review. No librarian was used to define search terms and only three databases were searched. Furthermore, the initial search, selection of articles, data extraction, and analysis was undertaken only by one author, potentially leading to the omission of relevant literature and data. The review also extended back to 1966, with some articles from the 1970s and 1980s included. Given the significant changes in medical treatment, social security systems, and society over the past decades, the generalizability of the findings may be limited.

Moreover, the majority of studies did not include a control group from the general population, which limited the ability to compare employment rates with the general population in the respective countries. Many studies were cross-sectional in design, which limits the evidence of causality between employment rate and having RA. However, the employment rate was approximately the same in high quality studies compared to all studies, which supports an association. A substantial number of studies relied on self-reported employment rates, introducing the potential for recall bias. Additionally, many studies did not account for all relevant risk factors for unemployment failing to control for all relevant confounders.

EULAR have made recommendation for point to consider when designing, analysing, and reporting of studies with work participation as an outcome domain in patients with inflammatory arthritis. These recommendations include study design, study duration, and the choice of work participation outcome domains (e.g., job type, social security system) and measurement instruments, the power to detect meaningful effects, interdependence among different work participation outcome domains (e.g., between absenteeism and presentism), the populations included in the analysis of each work participation outcome domain and relevant characteristics should be described. In longitudinal studies work-status should be regularly assessed and changes reported, and both aggregated results and proportions of predefined meaningful categories should be considered [ 128 ]. Only some of the studies in this review met the requirements for high quality studies. In both older and newer studies methodological deficiencies persisted in study design, analysis, and reporting of results, as recommended by EULAR.

Perspectives for future studies

Future research in this area should focus on developing and evaluating new strategies to address the ongoing challenges faced by patients with RA in maintaining employment. Despite many initiatives over the years, there has been no success in increasing employment rates for patients with RA in many countries. Therefore, there is a pressing need for controlled studies that investigated the effectiveness of interventions such as education, social support, and workplace adaptations in improving employment outcomes for these individuals.

This systematic review underscores the low employment rate among patients with RA. Key predictors of sustained employment include being younger, having higher educational level, short disease duration, and lower disease activity, along with fewer comorbidities. Importantly, the review reveals that the employment rate has not changed significantly across different time periods. To support patients with RA in maintaining their employment, a comprehensive approach that combines early clinical treatment with social support is crucial. This approach can play a pivotal role in helping patients with RA stay connected to the labour market.

Availability of data and materials

The datasets used and/or analyzed during the current study are available in the supplementary file.

Abbreviations

Rheumatoid arthritis

Methotrexate

Newcastle Ottawa Quality Assessment Scale

Standard deviation

Not analyzed

Not relevant

Disease activity

Health Assessment Questionnaire

Visual analog scale for pain

European Alliance of Associations for Rheumatology

American College of Rheumatology

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Lilli Kirkeskov & Katerina Bray

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LK performed the systematic research, including reading articles, performed the blinded quality assessment and the meta-analysis, and drafted and revised the article. KM performed the blinded quality assessment and the discussion afterwards of articles to be included in the research and the scores, and drafted and revised the article.

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Supplementary Information

Additional file 1: figure s1..

Employment; year of investigation.

Additional file 2: Figure S2.

Forest Plot of Comparison: Predictors for employment. Outcome: Younger or older age.

Additional file 3: Figure S3.

Forest Plot of Comparison: Predictors for employment. Outcome: >50 yr or <50 yr of age.

Additional file 4: Figure S4.

Forest Plot of Comparison: Predictors for employment. Outcome: Gender: Male or Female.

Additional file 5: Figure S5.

Forest Plot of Comparison: Predictors for employment. Outcome: Educational level: no college education or college education or higher.

Additional file 6: Figure S6.

Forest Plot of Comparison: Predictors for employment. Outcome: no comorbidities present or one or more comorbidities present.

Additional file 7: Figure S7.

Forest Plot of Comparison: Predictors for employment. Outcome: Ethnicity: Caucasian or other than Caucasian.

Additional file 8: Figure S8.

Forest Plot of Comparison: Predictors for employment. Outcome: Short or long disease duration.

Additional file 9: Figure S9.

Forest Plot of Comparison: Predictors for employment. Outcome: Low or high Health Assessment Questionnaire, HAQ-score.

Additional file 10: Figure S10.

Forest Plot of Comparison: Predictors for employment. Outcome: Low or high VAS-score.

Additional file 11: Figure S11.

Forest Plot of Comparison: Predictors for employment. Outcome: Job type: blue collar workers or other job types.

Additional file 12: Figure S12.

Forest Plot of Comparison: Predictors for employment. Outcome: No MTX or MTX.

Additional file 13: Figure S13.

Forest Plot of Comparison: Predictors for employment. Outcome: No biological or biological.

Additional file 14: Figure S14.

Forest Plot of Comparison: Predictors for employment. Outcome: No prednisolone or prednisolone.

Additional file 15: Figure S15.

Forest Plot of Comparison: Predictors for employment. Outcome: Low or high DAS score.

Additional file 16: Figure S16.

Forest Plot of Comparison: Predictors for employment. Outcome: Low or high SF 36-score.

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Kirkeskov, L., Bray, K. Employment of patients with rheumatoid arthritis - a systematic review and meta-analysis. BMC Rheumatol 7 , 41 (2023). https://doi.org/10.1186/s41927-023-00365-4

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Published on 12.4.2024 in Vol 26 (2024)

Application of AI in in Multilevel Pain Assessment Using Facial Images: Systematic Review and Meta-Analysis

Authors of this article:

Jian Huo 1 * , MSc ;
Yan Yu 2 * , MMS ;
Wei Lin 3 , MMS ;
Anmin Hu 2, 3, 4 , MMS ;
Chaoran Wu 2 , MD, PhD

1 Boston Intelligent Medical Research Center, Shenzhen United Scheme Technology Company Limited, Boston, MA, United States

2 Department of Anesthesia, Shenzhen People's Hospital, The First Affiliated Hospital of Southern University of Science and Technology, Shenzhen Key Medical Discipline, Shenzhen, China

3 Shenzhen United Scheme Technology Company Limited, Shenzhen, China

4 The Second Clinical Medical College, Jinan University, Shenzhen, China

*these authors contributed equally

Corresponding Author:

Chaoran Wu, MD, PhD

Department of Anesthesia

Shenzhen People's Hospital, The First Affiliated Hospital of Southern University of Science and Technology

Shenzhen Key Medical Discipline

No 1017, Dongmen North Road

Shenzhen, 518020

Phone: 86 18100282848

Email: [email protected]

Background: The continuous monitoring and recording of patients’ pain status is a major problem in current research on postoperative pain management. In the large number of original or review articles focusing on different approaches for pain assessment, many researchers have investigated how computer vision (CV) can help by capturing facial expressions. However, there is a lack of proper comparison of results between studies to identify current research gaps.

Objective: The purpose of this systematic review and meta-analysis was to investigate the diagnostic performance of artificial intelligence models for multilevel pain assessment from facial images.

Methods: The PubMed, Embase, IEEE, Web of Science, and Cochrane Library databases were searched for related publications before September 30, 2023. Studies that used facial images alone to estimate multiple pain values were included in the systematic review. A study quality assessment was conducted using the Quality Assessment of Diagnostic Accuracy Studies, 2nd edition tool. The performance of these studies was assessed by metrics including sensitivity, specificity, log diagnostic odds ratio (LDOR), and area under the curve (AUC). The intermodal variability was assessed and presented by forest plots.

Results: A total of 45 reports were included in the systematic review. The reported test accuracies ranged from 0.27-0.99, and the other metrics, including the mean standard error (MSE), mean absolute error (MAE), intraclass correlation coefficient (ICC), and Pearson correlation coefficient (PCC), ranged from 0.31-4.61, 0.24-2.8, 0.19-0.83, and 0.48-0.92, respectively. In total, 6 studies were included in the meta-analysis. Their combined sensitivity was 98% (95% CI 96%-99%), specificity was 98% (95% CI 97%-99%), LDOR was 7.99 (95% CI 6.73-9.31), and AUC was 0.99 (95% CI 0.99-1). The subgroup analysis showed that the diagnostic performance was acceptable, although imbalanced data were still emphasized as a major problem. All studies had at least one domain with a high risk of bias, and for 20% (9/45) of studies, there were no applicability concerns.

Conclusions: This review summarizes recent evidence in automatic multilevel pain estimation from facial expressions and compared the test accuracy of results in a meta-analysis. Promising performance for pain estimation from facial images was established by current CV algorithms. Weaknesses in current studies were also identified, suggesting that larger databases and metrics evaluating multiclass classification performance could improve future studies.

Trial Registration: PROSPERO CRD42023418181; https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=418181

Introduction

The definition of pain was revised to “an unpleasant sensory and emotional experience associated with, or resembling that associated with, actual or potential tissue damage” in 2020 [ 1 ]. Acute postoperative pain management is important, as pain intensity and duration are critical influencing factors for the transition of acute pain to chronic postsurgical pain [ 2 ]. To avoid the development of chronic pain, guidelines were promoted and discussed to ensure safe and adequate pain relief for patients, and clinicians were recommended to use a validated pain assessment tool to track patients’ responses [ 3 ]. However, these tools, to some extent, depend on communication between physicians and patients, and continuous data cannot be provided [ 4 ]. The continuous assessment and recording of patient pain intensity will not only reduce caregiver burden but also provide data for chronic pain research. Therefore, automatic and accurate pain measurements are necessary.

Researchers have proposed different approaches to measuring pain intensity. Physiological signals, for example, electroencephalography and electromyography, have been used to estimate pain [ 5 - 7 ]. However, it was reported that current pain assessment from physiological signals has difficulties isolating stress and pain with machine learning techniques, as they share conceptual and physiological similarities [ 8 ]. Recent studies have also investigated pain assessment tools for certain patient subgroups. For example, people with deafness or an intellectual disability may not be able to communicate well with nurses, and an objective pain evaluation would be a better option [ 9 , 10 ]. Measuring pain intensity from patient behaviors, such as facial expressions, is also promising for most patients [ 4 ]. As the most comfortable and convenient method, computer vision techniques require no attachments to patients and can monitor multiple participants using 1 device [ 4 ]. However, pain intensity, which is important for pain research, is often not reported.

With the growing trend of assessing pain intensity using artificial intelligence (AI), it is necessary to summarize current publications to determine the strengths and gaps of current studies. Existing research has reviewed machine learning applications for acute postoperative pain prediction, continuous pain detection, and pain intensity estimation [ 10 - 14 ]. Input modalities, including facial recordings and physiological signals such as electroencephalography and electromyography, were also reviewed [ 5 , 8 ]. There have also been studies focusing on deep learning approaches [ 11 ]. AI was applied in children and infant pain evaluation as well [ 15 , 16 ]. However, no study has focused on pain intensity measurement, and no comparison of test accuracy results has been made.

Current AI applications in pain research can be categorized into 3 types: pain assessment, pain prediction and decision support, and pain self-management [ 14 ]. We consider accurate and automatic pain assessment to be the most important area and the foundation of future pain research. In this study, we performed a systematic review and meta-analysis to assess the diagnostic performance of current publications for multilevel pain evaluation.

This study was registered with PROSPERO (International Prospective Register of Systematic Reviews; CRD42023418181) and carried out strictly following the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines [ 17 ] .

Study Eligibility

Studies that reported AI techniques for multiclass pain intensity classification were eligible. Records including nonhuman or infant participants or 2-class pain detection were excluded. Only studies using facial images of the test participants were accepted. Clinically used pain assessment tools, such as the visual analog scale (VAS) and numerical rating scale (NRS), and other pain intensity indicators, were rejected in the meta-analysis. Textbox 1 presents the eligibility criteria.

Study characteristics and inclusion criteria

Participants: children and adults aged 12 months or older
Setting: no restrictions
Index test: artificial intelligence models that measure pain intensity from facial images
Reference standard: no restrictions for systematic review; Prkachin and Solomon pain intensity score for meta-analysis
Study design: no need to specify

Study characteristics and exclusion criteria

Participants: infants aged 12 months or younger and animal subjects
Setting: no need to specify
Index test: studies that use other information such as physiological signals
Reference standard: other pain evaluation tools, e.g., NRS, VAS, were excluded from meta-analysis
Study design: reviews

Report characteristics and inclusion criteria

Year: published between January 1, 2012, and September 30, 2023
Language: English only
Publication status: published
Test accuracy metrics: no restrictions for systematic reviews; studies that reported contingency tables were included for meta-analysis

Report characteristics and exclusion criteria

Year: no need to specify
Language: no need to specify
Publication status: preprints not accepted
Test accuracy metrics: studies that reported insufficient metrics were excluded from meta-analysis

Search Strategy

In this systematic review, databases including PubMed, Embase, IEEE, Web of Science, and the Cochrane Library were searched until December 2022, and no restrictions were applied. Keywords were “artificial intelligence” AND “pain recognition.” Multimedia Appendix 1 shows the detailed search strategy.

Data Extraction

A total of 2 viewers screened titles and abstracts and selected eligible records independently to assess eligibility, and disagreements were solved by discussion with a third collaborator. A consentient data extraction sheet was prespecified and used to summarize study characteristics independently. Table S5 in Multimedia Appendix 1 shows the detailed items and explanations for data extraction. Diagnostic accuracy data were extracted into contingency tables, including true positives, false positives, false negatives, and true negatives. The data were used to calculate the pooled diagnostic performance of the different models. Some studies included multiple models, and these models were considered independent of each other.

Study Quality Assessment

All included studies were independently assessed by 2 viewers using the Quality Assessment of Diagnostic Accuracy Studies 2 (QUADAS-2) tool [ 18 ]. QUADAS-2 assesses bias risk across 4 domains, which are patient selection, index test, reference standard, and flow and timing. The first 3 domains are also assessed for applicability concerns. In the systematic review, a specific extension of QUADAS-2, namely, QUADAS-AI, was used to specify the signaling questions [ 19 ].

Meta-Analysis

Meta-analyses were conducted between different AI models. Models with different algorithms or training data were considered different. To evaluate the performance differences between models, the contingency tables during model validation were extracted. Studies that did not report enough diagnostic accuracy data were excluded from meta-analysis.

Hierarchical summary receiver operating characteristic (SROC) curves were fitted to evaluate the diagnostic performance of AI models. These curves were plotted with 95% CIs and prediction regions around averaged sensitivity, specificity, and area under the curve estimates. Heterogeneity was assessed visually by forest plots. A funnel plot was constructed to evaluate the risk of bias.

Subgroup meta-analyses were conducted to evaluate the performance differences at both the model level and task level, and subgroups were created based on different tasks and the proportion of positive and negative samples.

All statistical analyses and plots were produced using RStudio (version 4.2.2; R Core Team) and the R package meta4diag (version 2.1.1; Guo J and Riebler A) [ 20 ].

Study Selection and Included Study Characteristics

A flow diagram representing the study selection process is shown in ( Figure 1 ). After removing 1039 duplicates, the titles and abstracts of a total of 5653 papers were screened, and the percentage agreement of title or abstract screening was 97%. After screening, 51 full-text reports were assessed for eligibility, among which 45 reports were included in the systematic review [ 21 - 65 ]. The percentage agreement of the full-text review was 87%. In 40 of the included studies, contingency tables could not be made. Meta-analyses were conducted based on 8 AI models extracted from 6 studies. Individual study characteristics included in the systematic review are provided in Tables 1 and 2 . The facial feature extraction method can be categorized into 2 classes: geometrical features (GFs) and deep features (DFs). One typical method of extracting GFs is to calculate the distance between facial landmarks. DFs are usually extracted by convolution operations. A total of 20 studies included temporal information, but most of them (18) extracted temporal information through the 3D convolution of video sequences. Feature transformation was also commonly applied to reduce the time for training or fuse features extracted by different methods before inputting them into the classifier. For classifiers, support vector machines (SVMs) and convolutional neural networks (CNNs) were mostly used. Table 1 presents the model designs of the included studies.

a No temporal features are shown by – symbol, time information extracted from 2 images at different time by +, and deep temporal features extracted through the convolution of video sequences by ++.

b SVM: support vector machine.

c GF: geometric feature.

d GMM: gaussian mixture model.

e TPS: thin plate spline.

f DML: distance metric learning.

g MDML: multiview distance metric learning.

h AAM: active appearance model.

i RVR: relevance vector regressor.

j PSPI: Prkachin and Solomon pain intensity.

k I-FES: individual facial expressiveness score.

l LSTM: long short-term memory.

m HCRF: hidden conditional random field.

n GLMM: generalized linear mixed model.

o VLAD: vector of locally aggregated descriptor.

p SVR: support vector regression.

q MDS: multidimensional scaling.

r ELM: extreme learning machine.

s Labeled to distinguish different architectures of ensembled deep learning models.

t DCNN: deep convolutional neural network.

u GSM: gaussian scale mixture.

v DOML: distance ordering metric learning.

w LIAN: locality and identity aware network.

x BiLSTM: bidirectional long short-term memory.

a UNBC: University of Northern British Columbia-McMaster shoulder pain expression archive database.

b LOSO: leave one subject out cross-validation.

c ICC: intraclass correlation coefficient.

d CT: contingency table.

e AUC: area under the curve.

f MSE: mean standard error.

g PCC: Pearson correlation coefficient.

h RMSE: root mean standard error.

i MAE: mean absolute error.

j ICC: intraclass coefficient.

k CCC: concordance correlation coefficient.

l Reported both external and internal validation results and summarized as intervals.

Table 2 summarizes the characteristics of model training and validation. Most studies used publicly available databases, for example, the University of Northern British Columbia-McMaster shoulder pain expression archive database [ 57 ]. Table S4 in Multimedia Appendix 1 summarizes the public databases. A total of 7 studies used self-prepared databases. Frames from video sequences were the most used test objects, as 37 studies output frame-level pain intensity, while few measure pain intensity from video sequences or photos. It was common that a study redefined pain levels to have fewer classes than ground-truth labels. For model validation, cross-validation and leave-one-subject-out validation were commonly used. Only 3 studies performed external validation. For reporting test accuracies, different evaluation metrics were used, including sensitivity, specificity, mean absolute error (MAE), mean standard error (MSE), Pearson correlation coefficient (PCC), and intraclass coefficient (ICC).

Methodological Quality of Included Studies

Table S2 in Multimedia Appendix 1 presents the study quality summary, as assessed by QUADAS-2. There was a risk of bias in all studies, specifically in terms of patient selection, caused by 2 issues. First, the training data are highly imbalanced, and any method to adjust the data distribution may introduce bias. Next, the QUADAS-AI correspondence letter [ 19 ] specifies that preprocessing of images that changes the image size or resolution may introduce bias. However, the applicability concern is low, as the images properly represent the feeling of pain. Studies that used cross-fold validation or leave-one-out cross-validation were considered to have a low risk of bias. Although the Prkachin and Solomon pain intensity (PSPI) score was used by most of the studies, its ability to represent individual pain levels was not clinically validated; as such, the risk of bias and applicability concerns were considered high when the PSPI score was used as the index test. As an advantage of computer vision techniques, the time interval between the index tests was short and was assessed as having a low risk of bias. Risk proportions are shown in Figure 2 . For all 315 entries, 39% (124) were assessed as high-risk. In total, 5 studies had the lowest risk of bias, with 6 domains assessed as low risk [ 26 , 27 , 31 , 32 , 59 ].

Pooled Performance of Included Models

In 6 studies included in the meta-analysis, there were 8 different models. The characteristics of these models are summarized in Table S1 in Multimedia Appendix 2 [ 23 , 24 , 26 , 32 , 41 , 57 ]. Classification of PSPI scores greater than 0, 2, 3, 6, and 9 was selected and considered as different tasks to create contingency tables. The test performance is shown in Figure 3 as hierarchical SROC curves; 27 contingency tables were extracted from 8 models. The sensitivity, specificity, and LDOR were calculated, and the combined sensitivity was 98% (95% CI 96%-99%), the specificity was 98% (95% CI 97%-99%), the LDOR was 7.99 (95% CI 6.73-9.31) and the AUC was 0.99 (95% CI 0.99-1).

Subgroup Analysis

In this study, subgroup analysis was conducted to investigate the performance differences within models. A total of 8 models were separated and summarized as a forest plot in Multimedia Appendix 3 [ 23 , 24 , 26 , 32 , 41 , 57 ]. For model 1, the pooled sensitivity, specificity, and LDOR were 95% (95% CI 86%-99%), 99% (95% CI 98%-100%), and 8.38 (95% CI 6.09-11.19), respectively. For model 2, the pooled sensitivity, specificity, and LDOR were 94% (95% CI 84%-99%), 95% (95% CI 88%-99%), and 6.23 (95% CI 3.52-9.04), respectively. For model 3, the pooled sensitivity, specificity, and LDOR were 100% (95% CI 99%-100%), 100% (95% CI 99%-100%), and 11.55% (95% CI 8.82-14.43), respectively. For model 4, the pooled sensitivity, specificity, and LDOR were 83% (95% CI 43%-99%), 94% (95% CI 79%-99%), and 5.14 (95% CI 0.93-9.31), respectively. For model 5, the pooled sensitivity, specificity, and LDOR were 92% (95% CI 68%-99%), 94% (95% CI 78%-99%), and 6.12 (95% CI 1.82-10.16), respectively. For model 6, the pooled sensitivity, specificity, and LDOR were 94% (95% CI 74%-100%), 94% (95% CI 78%-99%), and 6.59 (95% CI 2.21-11.13), respectively. For model 7, the pooled sensitivity, specificity, and LDOR were 98% (95% CI 90%-100%), 97% (95% CI 87%-100%), and 8.31 (95% CI 4.3-12.29), respectively. For model 8, the pooled sensitivity, specificity, and LDOR were 98% (95% CI 93%-100%), 97% (95% CI 88%-100%), and 8.65 (95% CI 4.84-12.67), respectively.

Heterogeneity Analysis

The meta-analysis results indicated that AI models are applicable for estimating pain intensity from facial images. However, extreme heterogeneity existed within the models except for models 3 and 5, which were proposed by Rathee and Ganotra [ 24 ] and Semwal and Londhe [ 32 ]. A funnel plot is presented in Figure 4 . A high risk of bias was observed.

Pain management has long been a critical problem in clinical practice, and the use of AI may be a solution. For acute pain management, automatic measurement of pain can reduce the burden on caregivers and provide timely warnings. For chronic pain management, as specified by Glare et al [ 2 ], further research is needed, and measurements of pain presence, intensity, and quality are one of the issues to be solved for chronic pain studies. Computer vision could improve pain monitoring through real-time detection for clinical use and data recording for prospective pain studies. To our knowledge, this is the first meta-analysis dedicated to AI performance in multilevel pain level classification.

In this study, one model’s performance at specific pain levels was described by stacking multiple classes into one to make each task a binary classification problem. After careful selection in both the medical and engineering databases, we observed promising results of AI in evaluating multilevel pain intensity through facial images, with high sensitivity (98%), specificity (98%), LDOR (7.99), and AUC (0.99). It is reasonable to believe that AI can accurately evaluate pain intensity from facial images. Moreover, the study quality and risk of bias were evaluated using an adapted QUADAS-2 assessment tool, which is a strength of this study.

To investigate the source of heterogeneity, it was assumed that a well-designed model should have familiar size effects regarding different levels, and a subgroup meta-analysis was conducted. The funnel and forest plots exhibited extreme heterogeneity. The model’s performance at specific pain levels was described and summarized by a forest plot. Within-model heterogeneity was observed in Multimedia Appendix 3 [ 23 , 24 , 26 , 32 , 41 , 57 ] except for 2 models. Models 3 and 5 were different in many aspects, including their algorithms and validation methods, but were both trained with a relatively small data set, and the proportion of positive and negative classes was relatively close to 1. Because training with imbalanced data is a critical problem in computer vision studies [ 66 ], for example, in the University of Northern British Columbia-McMaster pain data set, fewer than 10 frames out of 48,398 had a PSPI score greater than 13. Here, we emphasized that imbalanced data sets are one major cause of heterogeneity, resulting in the poorer performance of AI algorithms.

We tentatively propose a method to minimize the effect of training with imbalanced data by stacking multiple classes into one class, which is already presented in studies included in the systematic review [ 26 , 32 , 42 , 57 ]. Common methods to minimize bias include resampling and data augmentation [ 66 ]. This proposed method is used in the meta-analysis to compare the test results of different studies as well. The stacking method is available when classes are only different in intensity. A disadvantage of combined classes is that the model would be insufficient in clinical practice when the number of classes is low. Commonly used pain evaluation tools, such as VAS, have 10 discrete levels. It is recommended that future studies set the number of pain levels to be at least 10 for model training.

This study is limited for several reasons. First, insufficient data were included because different performance metrics (mean standard error and mean average error) were used in most studies, which could not be summarized into a contingency table. To create a contingency table that can be included in a meta-analysis, the study should report the following: the number of objects used in each pain class for model validation, and the accuracy, sensitivity, specificity, and F 1 -score for each pain class. This table cannot be created if a study reports the MAE, PCC, and other commonly used metrics in AI development. Second, a small study effect was observed in the funnel plot, and the heterogeneity could not be minimized. Another limitation is that the PSPI score is not clinically validated and is not the only tool that assesses pain from facial expressions. There are other clinically validated pain intensity assessment methods, such as the Faces Pain Scale-revised, Wong-Baker Faces Pain Rating Scale, and Oucher Scale [ 3 ]. More databases could be created based on the above-mentioned tools. Finally, AI-assisted pain assessments were supposed to cover larger populations, including incommunicable patients, for example, patients with dementia or patients with masked faces. However, only 1 study considered patients with dementia, which was also caused by limited databases [ 50 ].

AI is a promising tool that can help in pain research in the future. In this systematic review and meta-analysis, one approach using computer vision was investigated to measure pain intensity from facial images. Despite some risk of bias and applicability concerns, CV models can achieve excellent test accuracy. Finally, more CV studies in pain estimation, reporting accuracy in contingency tables, and more pain databases are encouraged for future studies. Specifically, the creation of a balanced public database that contains not only healthy but also nonhealthy participants should be prioritized. The recording process would be better in a clinical environment. Then, it is recommended that researchers report the validation results in terms of accuracy, sensitivity, specificity, or contingency tables, as well as the number of objects for each pain class, for the inclusion of a meta-analysis.

Acknowledgments

WL, AH, and CW contributed to the literature search and data extraction. JH and YY wrote the first draft of the manuscript. All authors contributed to the conception and design of the study, the risk of bias evaluation, data analysis and interpretation, and contributed to and approved the final version of the manuscript.

Data Availability

The data sets generated during and analyzed during this study are available in the Figshare repository [ 67 ].

Conflicts of Interest

None declared.

PRISMA checklist, risk of bias summary, search strategy, database summary and reported items and explanations.

Study performance summary.

Forest plot presenting pooled performance of subgroups in meta-analysis.

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Abbreviations

Edited by A Mavragani; submitted 26.07.23; peer-reviewed by M Arab-Zozani, M Zhang; comments to author 18.09.23; revised version received 08.10.23; accepted 28.02.24; published 12.04.24.

©Jian Huo, Yan Yu, Wei Lin, Anmin Hu, Chaoran Wu. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 12.04.2024.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in the Journal of Medical Internet Research, is properly cited. The complete bibliographic information, a link to the original publication on https://www.jmir.org/, as well as this copyright and license information must be included.

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Hippokratia
v.14(Suppl 1); 2010 Dec

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.

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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.

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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 ).

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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 ).

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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 .

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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.

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COMMENTS

How to conduct a meta-analysis in eight steps: a practical guide
Choosing which meta-analytical method to use is directly connected to the research question of the meta-analysis. Research questions in meta-analyses can address a relationship between constructs or an effect of an intervention in a general manner, or they can focus on moderating or mediating effects.
Meta-Analytic Methodology for Basic Research: A Practical Guide
The goal of this study is to present a brief theoretical foundation, computational resources and workflow outline along with a working example for performing systematic or rapid reviews of basic research followed by meta-analysis. Conventional meta-analytic techniques are extended to accommodate methods and practices found in basic research.
Introduction to systematic review and meta-analysis
It is easy to confuse systematic reviews and meta-analyses. A systematic review is an objective, reproducible method to find answers to a certain research question, by collecting all available studies related to that question and reviewing and analyzing their results. A meta-analysis differs from a systematic review in that it uses statistical ...
Meta-Analysis
Definition. "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 ...
Methodological Guidance Paper: High-Quality Meta-Analysis in a
The term meta-analysis was first used by Gene Glass (1976) in his presidential address at the AERA (American Educational Research Association) annual meeting, though Pearson (1904) used methods to combine results from studies on the relationship between enteric fever and mortality in 1904. The 1980s was a period of rapid development of statistical methods (Cooper & Hedges, 2009) leading to the ...
Chapter 10: Analysing data and undertaking meta-analyses
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.
PDF How to conduct a meta-analysis in eight steps: a practical guide
Meta-analysis is a central method for knowledge accumulation in many scien-tic elds (Aguinis et al. 2011c; Kepes et al. 2013). Similar to a narrative review, it serves as a synopsis of a research question or eld. However, going beyond a narra-tive summary of key ndings, a meta-analysis adds value in providing a quantitative
Ten simple rules for carrying out and writing meta-analyses
Introduction. In the context of evidence-based medicine, meta-analyses provide novel and useful information [], as they are at the top of the pyramid of evidence and consolidate previous evidence published in multiple previous reports [].Meta-analysis is a powerful tool to cumulate and summarize the knowledge in a research field [].Because of the significant increase in the published ...
Meta-analysis and the science of research synthesis
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 ...
Meta-Analysis (Chapter 29)
Meta-analysis is a well-established approach to integrating research findings, with a long history in the sciences and in psychology in particular. Its use in summarizing research findings has special significance given increasing concerns about scientific replicability, but it has other important uses as well, such as integrating information ...
A Guide to Conducting a Meta-Analysis
Abstract. Meta-analysis is widely accepted as the preferred method to synthesize research findings in various disciplines. This paper provides an introduction to when and how to conduct a meta-analysis. Several practical questions, such as advantages of meta-analysis over conventional narrative review and the number of studies required for a ...
Getting Started
A systematic review may include a meta-analysis. For details about carrying out systematic reviews, see the Guides and Standards section of this guide. Is my research topic appropriate for systematic review methods? A systematic review is best deployed to test a specific hypothesis about a healthcare or public health intervention or exposure.
Research Guides: Study Design 101: Meta-Analysis
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.
Meta-analysis
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 ...
Meta‐analysis and traditional systematic literature reviews—What, why
Meta-analysis is a research method for systematically combining and synthesizing findings from multiple quantitative studies in a research domain. Despite its importance, most literature evaluating meta-analyses are based on data analysis and statistical discussions. This paper takes a holistic view, comparing meta-analyses to traditional ...
Meta-Analysis: A Quantitative Approach to Research Integration
Additional statistical research should include study of the impact of outliers on the meta-analysis and the potential insight that they could provide into a research question . Statistically valid methods to combine data across studies of varying quality and design, including data from case-control studies, will enable metaanalysts to maximize ...
How to do a Meta Analysis: Methodology, Pros & Cons
Meta-analyses are used by researchers to review large and sometimes complex research. In a meta-analysis, the tested hypothesis and the results are essential because meta-analysis is a delicate method. Meta-Analysis has the ability to be totally objective in analyzing and evaluating research outcomes.
Understanding meta-analysis
It outlines the conceptual approach to meta-analysis, graphical presentations and the key meta-analysis methods that are recommended. Meta-analysis of test accuracy studies provides summaries of the results of relevant included studies, providing estimates of the average diagnostic accuracy of a test or tests, the uncertainty of these estimates ...
Introduction to Procedures and Methods of Meta-Analysis
Abstract and Figures. Meta-Analysis is the quantitative integration of research findings with the help of statistical tools. Reviewing academic literature on meta-analysis and research synthesis ...
Relationship between triglyceride-glucose index and new-onset
This meta-analysis comprised a total of 35 848 participants across seven investigations Citation 13-19. The mean age of participants in the seven trials varied between 35.8 and 57.2 years. The mean body mass index (BMI) varied between 20.9 and 27.2 kg/m 2. The duration of the follow-up period varied between 1.7 and 9 years.
A brief introduction of meta‐analyses in clinical practice and research
Combining the methodology of cumulative meta‐analysis with the technique of formal sequential testing, which can sequentially evaluate the available evidence at consecutive interim steps during the data collection: ... The primary limitation of a meta‐analysis is missing related research. Even in the ideal case in which all relevant studies ...
Employment of patients with rheumatoid arthritis
LK performed the systematic research, including reading articles, performed the blinded quality assessment and the meta-analysis, and drafted and revised the article. KM performed the blinded quality assessment and the discussion afterwards of articles to be included in the research and the scores, and drafted and revised the article.
Meta-Analysis
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.
Journal of Medical Internet Research
Objective: The purpose of this systematic review and meta-analysis was to investigate the diagnostic performance of artificial intelligence models for multilevel pain assessment from facial images. Methods: The PubMed, Embase, IEEE, Web of Science, and Cochrane Library databases were searched for related publications before September 30, 2023.
Genes
Background: Normal tension glaucoma (NTG) is becoming a more and more serious problem, especially in Asia. But the pathological mechanisms are still not illustrated clearly. We carried out this research to uncover the gene polymorphisms with NTG. Methods: We searched in Web of Science, Embase, Pubmed and Cochrane databases for qualified case-control studies investigating the association ...
Meta-analysis in medical research
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 ...

Meta-Analysis – Guide with Definition, Steps & Examples

What is Meta-Analysis

When Should you Conduct a Meta-Analysis?

Elements of a Meta-Analysis

Characteristics:

Strengths:

Criticisms:

Steps of Conducting the Meta-Analysis

Step 1: Research Question

Step 2: Systematic Review

Step 3: Data Extraction

Step 4: Standardisation and Weighting Studies

Step 5: Absolute Effect Estimation

Forest Plot

Relevance to Practice and Research

Methods and Assumptions in Meta-Analysis

Difference Between Meta-Analysis and Systematic Reviews

Software Packages For Meta-Analysis

Assessing the Quality of Meta-Analysis

Hire an Expert Writer

Examples of Meta-Analysis

Frequently Asked Questions

Why is meta-analysis important?

What is an example of a meta-analysis?

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

Is meta-analysis qualitative or quantitative?

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Key Points:

10.1 Do not start here!

10.2 Introduction to meta-analysis

10.2.1 Principles of meta-analysis

10.3 A generic inverse-variance approach to meta-analysis

10.3.1 Fixed-effect method for meta-analysis

10.3.2 Random-effects methods for meta-analysis

10.3.3 Performing inverse-variance meta-analyses

10.4 Meta-analysis of dichotomous outcomes

10.4.1 Mantel-Haenszel methods

10.4.2 Peto odds ratio method

10.4.3 Which effect measure for dichotomous outcomes?

10.4.4 Meta-analysis of rare events

10.4.4.1 Studies with no events in one or more arms

10.4.4.2 Studies with no events in either arm

10.4.4.3 Validity of methods of meta-analysis for rare events

10.5 Meta-analysis of continuous outcomes

10.5.1 Which effect measure for continuous outcomes?

10.5.2 Meta-analysis of change scores

10.5.3 Meta-analysis of skewed data

10.6 Combining dichotomous and continuous outcomes

10.7 Meta-analysis of ordinal outcomes and measurement scale s

10.8 Meta-analysis of counts and rates

10.9 Meta-analysis of time-to-event outcomes

10.10 Heterogeneity

10.10.2 Identifying and measuring heterogeneity

10.10.3 Strategies for addressing heterogeneity

10.10.4 Incorporating heterogeneity into random-effects models

10.10.4.1 Fixed or random effects?

10.10.4.2 Interpretation of random-effects meta-analyses

10.10.4.3 Prediction intervals from a random-effects meta-analysis

10.10.4.4 Implementing random-effects meta-analyses

10.11 Investigating heterogeneity

10.11.2 What are subgroup analyses?

10.11.3 Undertaking subgroup analyses

10.11.3.1 Is the effect different in different subgroups?

10.11.4 Meta-regression

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

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

10.11.5.2 Specify characteristics in advance

10.11.5.3 Select a small number of characteristics

10.11.5.4 Ensure there is scientific rationale for investigating each characteristic

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

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

10.11.6 Interpretation of subgroup analyses and meta-regressions

10.11.7 Investigating the effect of underlying risk

10.11.8 Dose-response analyses

10.12 Missing data

10.12.2 General principles for dealing with missing data

10.12.3 Dealing with missing outcome data from individual participants

10.13 Bayesian approaches to meta-analysis

10.14 Sensitivity analyses