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A Re-Evaluation of Random-Effects Meta-Analysis
Open accessAbstract
Summary: Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of ‘set shifting’ ability in people with eating disorders.
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TL;DR
This paper re-evaluates random-effects meta-analysis, arguing that inference should address the whole distribution of effects—especially prediction—rather than only the mean effect. It proposes a simple classical prediction interval and illustrates the issues with 14 studies of set-shifting ability in eating disorders.
Key findings
- Focusing only on the mean of the random-effects distribution is insufficient: two meta-analytic data sets can produce identical mean estimates and standard errors while differing greatly in heterogeneity, so τ² and the whole distribution matter.
- Distribution-free classical methods can estimate μ and τ² but cannot satisfactorily address prediction; the paper proposes an approximate prediction interval using a t-distribution with k−2 degrees of freedom.
- In the 14-study set-shifting example, heterogeneity was Q=16.73, df=13, P=0.02, I²=22%, and τ²=0.022; the classical random-effects interval was 0.19–0.53, while the approximate prediction interval for a new study ranged from −0.01 to 0.74.
- Bayesian normal random-effects analysis gave μ median 0.36 (95% credible interval 0.18–0.55), θ_new median 0.36 (−0.12–0.84), P(θ_new<0)=0.950, and τ² median 0.023 (0.000024–0.196); Bayesian credible intervals were wider because uncertainty in τ² was properly accounted for.
Methods
- The paper is a methodological re-evaluation structured around estimation, prediction, and hypothesis testing, comparing distribution-free, classical parametric, Bayesian, and non-normal/flexible random-effects approaches.
- The example uses 14 comparative studies of set-shifting ability in people with eating disorders versus healthy controls, taken from Roberts et al. (2007), with effect sizes as standardized differences in means and their standard errors.
- Analyses include classical inverse-variance random-effects meta-analysis with a moment estimate of between-study variance, and Bayesian normal random-effects meta-analysis via MCMC in WinBUGS with a uniform prior for τ (>0) and a vague N(0,10³) prior for μ; sensitivity analyses used a t-distribution with 4 degrees of freedom, an inverse gamma prior, and a shrinkage prior.
Limitations
- Stated: the Bayesian approach has problems including computational intensity and sensitivity to a priori judgements; prior choice can substantially affect results; model uncertainty is not accounted for; the normal random-effects assumption is strong and usually made without convincing evidence; few studies make τ² and μ imprecise; separating diversity from bias is difficult; and caution is warranted with funnel plot asymmetry.
- Stated: the example data were available only as effect sizes and confidence intervals, from which standard errors were calculated; more detailed data should be explicitly modelled when available.
- Evident: the example has only 14 studies and some large within-study standard errors; the paper notes that meta-analyses with very small numbers of studies (2–4) pose particular problems, and prediction intervals depend on the number of studies and within-study standard errors.
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52 Own interpretation · 22 Not checked yet · 12 No basis given · 7 Own result
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In the paper
“The approximate prediction interval (12) for the true effect in a new study, however, ranges from −0.01 to 0.74, which is slightly less convincing.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
In the paper
“Alternatively using an inverse gamma distribution for τ2 with parameters 0.001 and 0.001 (Smith et al., 1995) produces a prediction interval from −0.008 to 0.73 (P(θnew<0)=0.973)”
§ A re-evaluation of random-effects meta-analysis > 7 Example
What the sources say
- Not checked yetcites Smith et al., 1995 source
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“| τ2 | 0.023 | (0.000024, 0.196) | — |”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
In the paper
“There is some heterogeneity between the effect sizes, accounting for 22% of the variation in point estimates by using the statistic I2 (Higgins and Thompson, 2002).”
§ A re-evaluation of random-effects meta-analysis > 7 Example
What the sources say
- Not checked yetcites Higgins and Thompson, 2002
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A random-effects meta-analysis reveals a statistically significant benefit on average, based on the inference in equation (13) regarding μ alone.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
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In the paper
“It is evident from Table 1, as well as from the estimated effect sizes, plotted with 95% confidence intervals in Fig. 2, that the majority of trials indicate greater set shifting deficiency in people with eating disorders.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
In the paper
“Correspondingly, the test for qualitative interaction (9) produces a statistically non-significant test statistic Q*=2.56, compared with a critical value of 14.15 for a significance level of 5% (Gail and Simon, 1985).”
§ A re-evaluation of random-effects meta-analysis > 7 Example
What the sources say
- Not checked yetcites Gail and Simon, 1985 source
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
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In the paper
“However, such an assumption of homogeneity can seldom be made for studies in the biomedical and social sciences.”
§ A re-evaluation of random-effects meta-analysis > 1 Introduction
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“This property is shared with the conventional test from a random-effects meta-analysis, i.e. of hypothesis (2) against”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.3 Statistical tests in the presence of heterogeneity
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Estimation of τ2 is just as important.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.1 Estimation in random-effects meta-analysis
plain- Asserted: passes — The authors put it forward as true.
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- It may state two separate claims as one. 25
- Probably not a substantial claim. 29
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In the paper
“Various sensitivity analyses have small effects on the results, though they do not materially affect the conclusions from the Bayesian meta-analysis.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“using the shrinkage prior that was advocated by DuMouchel and Normand (2000) produces a prediction interval from −0.009 to 0.72 (P(θnew<0)=0.973)”
§ A re-evaluation of random-effects meta-analysis > 7 Example
What the sources say
- Not checked yetcites DuMouchel and Normand (2000)
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“The estimate of the heterogeneity variance is 0.022 and the test for heterogeneity is statistically significant at conventional levels of significance.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using a t-distribution with 4 degrees of freedom for the random effects yields a prediction interval from −0.16 to 0.89 (P(θnew<0)=0.947).”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
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In the paper
“Results for μ and θnew are comparable with the classical results, with credible intervals being wider because the Bayesian analyses properly account for uncertainty in the estimation of τ2.”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
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In the paper
“| μ | 0.36 | (0.18, 0.55) | 0.999 |”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| θnew | 0.36 | (−0.12, 0.84) | 0.950 |”
§ A re-evaluation of random-effects meta-analysis > 7 Example
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The random effects in the meta-analysis are normally distributed.
None of the sources cited for this claim have been checked yet.
In the paper
“Although sources of heterogeneity should ideally be investigated (Thompson, 1994), selection of covariates to explain heterogeneity can be difficult, both practically (Higgins et al., 2002) and theoretically (Thompson and Higgins, 2002).”
§ A re-evaluation of random-effects meta-analysis > 1 Introduction
What the sources say
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Realistic interpretation of predictions from a random-effects model can, however, be difficult.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.2 Prediction using random-effects meta-analysis
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This variance explicitly describes the extent of the heterogeneity and has a crucial role in assessing the degree of consistency of effects across studies, which is an element of random-effects meta-analysis that often receives too little attention.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.1 Estimation in random-effects meta-analysis
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
In the paper
“However, a single parameter cannot adequately summarize heterogeneous effects (Raudenbush and Bryk, 1985) and so focusing on μ alone is usually insufficient.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.1 Estimation in random-effects meta-analysis
What the sources say
- Not checked yetcites Raudenbush and Bryk, 1985 source
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although often useful, the test may be misleading if there is heterogeneity and in particular will not reject hypothesis (1) if effects are variable and centred on 0.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.3 Statistical tests in the presence of heterogeneity
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“Meta-analyses are often built on an assumption that directions of effect are consistent across studies (Peto, 1987), yet formal tests of this important supposition are not routinely undertaken.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.3 Statistical tests in the presence of heterogeneity
What the sources say
- Not checked yetcites Peto, 1987 source
plain- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“An important rationale for meta-analyses is the possibility of increased power, compared with the individual studies, to detect moderate effects.”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.3 Statistical tests in the presence of heterogeneity
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“We have argued that such a null hypothesis is typically untenable and have discouraged the use of homogeneity tests in favour of quantifying the extent of heterogeneity (Higgins and Thompson, 2002).”
§ A re-evaluation of random-effects meta-analysis > 2 Important questions to address in a random-effects meta-analysis > 2.3 Statistical tests in the presence of heterogeneity
What the sources say
- Not checked yetcites Higgins and Thompson, 2002
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Point estimation of μ and τ2 poses no problem, although confidence intervals rely on approximating distributions, sometimes based on the central limit theorem, which may not be realistic when there are few studies.”
§ A re-evaluation of random-effects meta-analysis > 3 Meeting the important objectives with no distributional assumption for the random effects > 3.6 Summarizing remarks
hedgedconditional- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: The available effect estimates are unbiased for the study-specific effects θi.
- The authors state this as an assumption: The estimated variances may be used in place of the true variances.
In the paper
“However, NPML has been noted to be unstable (Van Houwelingen et al., 1993) and has not been widely adopted.”
§ A re-evaluation of random-effects meta-analysis > 6 Non-normal and flexible assumptions for the random effects
What the sources say
- Not checked yetcites Van Houwelingen et al., 1993 source
plain- Asserted: passes — The authors put it forward as true.
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None of the sources cited for this claim have been checked yet.
In the paper
“NPML procedures provide a discrete distribution that is based on a finite number of mass points (Laird, 1978; Böhning, 2005).”
§ A re-evaluation of random-effects meta-analysis > 6 Non-normal and flexible assumptions for the random effects
What the sources say
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The assumption of a normal distribution for the random-effects distribution allows the calculation of confidence intervals and prediction intervals.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.6 Summarizing remarks
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
- The authors state this as an assumption: The random-effects distribution is normal.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A second potential advantage of a Bayesian approach is the intuitive interpretation of posterior distributions in terms of probability, including the ready availability of probabilities that effects exceed specified levels.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.6 Summarizing remarks
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A particular advantage of the NPML approach is its ability to detect and incorporate outliers.”
§ A re-evaluation of random-effects meta-analysis > 6 Non-normal and flexible assumptions for the random effects
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Bayesian probabilities can address a variety of questions more readily than classical hypothesis tests.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.5 Testing
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Whatever the reason for it, an asymmetric funnel plot leads necessarily to a difference in point estimates between common effect and random-effects meta-analyses (using standard inverse variance methods), because random-effects methods give relatively more weight to less precise studies.”
§ A re-evaluation of random-effects meta-analysis > 8 Some special considerations in random-effects meta-analysis > 8.2 Reporting biases and small study effects
boosteddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Meta-analyses of a large number of large studies lend themselves to relatively complex models, since there may be strong evidence against a normal distribution assumption for the random effect.”
§ A re-evaluation of random-effects meta-analysis > 6 Non-normal and flexible assumptions for the random effects
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The posterior distribution for the underlying mean μ is readily available from a Bayesian meta-analysis.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.2 Mean effect
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In practice, it can be difficult to separate diversity from bias, and it is partly this lack of identifiability that often necessitates the use of the conventional random-effects model.”
§ A re-evaluation of random-effects meta-analysis > 8 Some special considerations in random-effects meta-analysis > 8.1 Diversity and bias
plainconditional- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: The true (unbiased) effects Φi follow a normal distribution across studies.
- The authors state this as an assumption: The study-specific bias components βi follow a normal distribution.
- The authors state this as an assumption: The diversity and bias components are uncorrelated.
- The authors state this as an assumption: The effect being evaluated in the ith study is the sum of the true effect and bias: θi=Φi+βi.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The posterior distributions for the study-specific effects θi are readily available from a Bayesian analysis. These provide fully Bayesian shrunken estimates, in which inference for each particular study is performed by ‘borrowing strength’ from the other studies.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.3 Study effects
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“An important distinction to make when considering heterogeneity of effect sizes is between the effects of diversity (variation in populations, interventions, exposures, outcome measures etc.) and bias (variation in the quality of the design and conduct of the studies) (Glasziou and Sanders, 2002; Greenland and O'Rourke, 2001).”
§ A re-evaluation of random-effects meta-analysis > 8 Some special considerations in random-effects meta-analysis > 8.1 Diversity and bias
What the sources say
- Not checked yetcites Glasziou and Sanders, 2002
- Not checked yetcites Greenland and O'Rourke, 2001
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“No model for the random-effects distribution will be ‘true’, and we might seek a parsimonious model that adequately fits the observed data.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, this uncertainty does not extend to the choice of model for the random effects, which is more difficult to defend empirically when there are few studies.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.6 Summarizing remarks
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The random-effects distribution is normal.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Tests for heterogeneity have low power when there are few studies, and heterogeneity may be just as likely for small numbers of studies as it is for large numbers of studies.”
§ A re-evaluation of random-effects meta-analysis > 8 Some special considerations in random-effects meta-analysis > 8.3 Small numbers of studies
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“For example, when 2×2 contingency tables are available for binary outcomes, meta-analyses are appropriately performed by using binomial likelihoods (Smith et al., 1995; Warn et al., 2002).”
§ A re-evaluation of random-effects meta-analysis > 7 Example
What the sources say
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Bayesian posterior probabilities in particular can depend heavily on the distribution of the assumed likelihood and prior specification.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.6 Summarizing remarks
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
- The authors state this as an assumption: The prior distributions of μ and τ2 are independent.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The derivation of the predictive distributions for the effect θnew in a future study has received little methodological attention in a frequentist context.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.4 Prediction
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
In the paper
“However, it is unclear how prior distributions should be specified, which is an important limitation since Bayes factors can be very sensitive to them (Kass and Raftery, 1995).”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.5 Testing
What the sources say
- Not checked yetcites Kass and Raftery, 1995 source
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such an infinite population does not in reality exist, although the construct does allow inference about treatment effects to be extended to a broader population than the studies at hand.”
§ A re-evaluation of random-effects meta-analysis > 4 Classical parametric and Bayesian approaches to random-effects meta-analysis
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The true predictive distribution is a complex function of the degree of heterogeneity, the number of studies and the within-study standard errors.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.6 Summarizing remarks
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A particular advantage is that they may be used to provide evidence specifically in favour of a null hypothesis.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.5 Testing
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“From a classical point of view, interpretation of parametric random-effects meta-analysis is formally in the context of an imaginary ‘universe’, or ‘population’ of similar effects from which the effects in the observed studies are independently and identically sampled.”
§ A re-evaluation of random-effects meta-analysis > 4 Classical parametric and Bayesian approaches to random-effects meta-analysis
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A realistic predictive distribution must recognize, however, that τ2 is estimated, usually from a small number of studies, and imprecision in affects both terms in the variance of θnew.”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects > 5.4 Prediction
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: Approximately, the predictive distribution of θnew follows a t-distribution with k−2 degrees of freedom.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Requiring only two parameters for its full specification, the most parsimonious choice is also the conventional choice, where f(Φ) is chosen to be a normal distribution: (10)”
§ A re-evaluation of random-effects meta-analysis > 5 Meeting the important objectives with a normal assumption for the random effects
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Flexible distributions such as Bayesian semiparametric models are available, although it remains difficult to implement non-normal distributions outside an MCMC approach to the analysis.”
§ A re-evaluation of random-effects meta-analysis > 9 Discussion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A Bayesian approach has the additional advantages of flexibility, allowing incorporation of full uncertainty in all parameters (but not uncertainty in the model) and of yielding more readily interpretable inferences.”
§ A re-evaluation of random-effects meta-analysis > 9 Discussion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In many situations this is the most feasible assumption given the limited number of studies and the lack of strong evidence for or against the assumption.”
§ A re-evaluation of random-effects meta-analysis > 9 Discussion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus the rationale is not strong for opting for a common effect model in this situation.”
§ A re-evaluation of random-effects meta-analysis > 8 Some special considerations in random-effects meta-analysis > 8.3 Small numbers of studies
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Meta-analyses of very few studies need not ‘default’ to a common effect model, since informative prior distributions for the extent of heterogeneity can be incorporated in a simple Bayesian approach.”
§ A re-evaluation of random-effects meta-analysis > 9 Discussion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“Furthermore, certain common effect approaches have practical advantages over random-effects methods. For example, they are easier to implement, and the one-step ‘Peto’ method has been observed to have desirable properties when binary events are rare (Bradburn et al., 2006).”
§ A re-evaluation of random-effects meta-analysis > 9 Discussion
What the sources say
- Not checked yetcites Bradburn et al., 2006 source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The authors state this as an assumption.
If an effect exists then heterogeneity exists, although it may be negligible.
“We assume a priori that if an effect exists then heterogeneity exists, although it may be negligible.”
The authors state this as an assumption.
The available effect estimates are unbiased for the study-specific effects θi.
“For generality, the situation that we address assumes only the availability of effect estimates that are unbiased for θi (i =1,…,k), with sampling variance (i.e. squared standard error) .”
The authors state this as an assumption.
The estimated variances may be used in place of the true variances.
“We shall follow the conventional assumption that estimates (which are independent of ) may be used in place of the true variances, and we use the two interchangeably.”
The authors state this as an assumption.
The effect estimates from each study are normally distributed.
“We are willing to assume normality of the effect estimates from each study, so(6)”
The authors state this as an assumption.
The prior distributions of μ and τ2 are independent.
“It is standard to assume prior independence of μ and τ2.”
The authors state this as an assumption.
Approximately, the predictive distribution of θnew follows a t-distribution with k−2 degrees of freedom.
“Again taking a t-distribution with k−2 degrees of freedom, we assume that, approximately, (11)”
The authors state this as an assumption.
The between-study variance is common to each study.
“The assumption of a common between-study variance for each study is a strong one that we return to in Section 8.1.”
The authors state this as an assumption.
The underlying effects are exchangeable.
“Fundamental to a Bayesian approach to random-effects meta-analysis is the concept of exchangeability. Exchangeability represents a judgement that the treatment effects may be non-identical but their magnitudes cannot be differentiated a priori (Skene and Wakefield, 1990; Gelman et al., 1995).”
The authors state this as an assumption.
The random-effects distribution is normal.
“Requiring only two parameters for its full specification, the most parsimonious choice is also the conventional choice, where f(Φ) is chosen to be a normal distribution: (10)”
The authors state this as an assumption.
The random effects in the meta-analysis are normally distributed.
“by assuming a normal distribution for the random effects”
“Using a normal distribution for the underlying effects in different studies is a strong assumption”
The authors state this as an assumption.
The true (unbiased) effects Φi follow a normal distribution across studies.
“we represent this by using a normal distribution across the ‘true’ (unbiased) effects”
The authors state this as an assumption.
The study-specific bias components βi follow a normal distribution.
“Suppose that the study-specific bias components follow a normal distribution such that .”
The authors state this as an assumption.
The diversity and bias components are uncorrelated.
“assuming that the diversity and bias components are uncorrelated”
The authors state this as an assumption.
The effect being evaluated in the ith study is the sum of the true effect and bias: θi=Φi+βi.
“The effect being evaluated in the ith study, θi, is the sum of the true effect and bias: θi=Φi+βi.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“In addition to the pooled 95% CI, a 95% prediction interval (PI) was calculated to reflect the expected dispersion of true effects in future clinical settings (20,21).”
From Comparison of point‑of‑care HbA1c devices with laboratory HPLC methods: A systematic review and meta‑analysis (2026) · cites this paper as [21]
The cited source says what the claim attributes to it.
In the citing paper
“a 95% prediction interval (PI) was calculated to reflect the expected dispersion of true effects in future clinical settings (20,21).”
From Comparison of point‑of‑care HbA1c devices with laboratory HPLC methods: A systematic review and meta‑analysis (2026) · cites this paper as [21]
In the citing paper
“This is particularly relevant when confronting sparse data, multiple comparisons, collinearity, or non-identification, and for deriving PI.51”
From A framework for meta-analysis of prediction model studies with binary and time-to-event outcomes (2019) · cites this paper as [51]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ A re-evaluation of random-effects meta-analysis > 7 Example
“Note that P(θnew<0)=0.950 in Table 2 corresponds to the point at which the full curve in Fig. 3(b) crosses the vertical axis (at approximately 5% probability)”
§ A re-evaluation of random-effects meta-analysis > 7 Example
“| Parameter | Median | 95% credible interval | P(parameter > 0) | | --- | --- | --- | --- | | μ | 0.36 | (0.18, 0.55) | 0.999 | | θnew | 0.36 | (−0.12, 0.84) | 0.950 |”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ A re-evaluation of random-effects meta-analysis > 7 Example
“Random-effects meta-analysis: standardized mean difference (95% credible interval 0.19–0.53); U*=4.23 (P =2×10−5); .”
§ A re-evaluation of random-effects meta-analysis > 7 Example
“Classical normal random-effects meta-analysis results as traditionally presented appear at the bottom of Table 1.”
Citations
Cites
Bias in meta-analysis detected by a simple, graphical test
Egger, M., Smith, G. D., Schneider, M., & Minder, C. (1997) · BMJ · doi:10.1136/bmj.315.7109.629 · Cited by 56,722 · cited 1×
“This may reflect publication bias, or correlation between study size and another important covariate such as quality of study (Egger et al., 1997).”
BackgroundMeta-analysis in clinical trials
DerSimonian, R., & Laird, N. (1986) · Controlled Clinical Trials · doi:10.1016/0197-2456(86)90046-2 · Cited by 39,552 · cited 6×
“Heterogeneity Several estimators of the heterogeneity variance τ2 are available that are based on normal likelihoods, including iterative maximum likelihood and restricted maximum likelihood estimates (DerSimonian and Laird, 1986; DerSimonian and Kacker, 2007).”
MethodInfluentialQuantifying heterogeneity in a meta‐analysis
Higgins, J. P. T., & Thompson, S. G. (2002) · Statistics in Medicine · doi:10.1002/sim.1186 · Cited by 36,763 · cited 10×
“Confidence intervals for measures of inconsistency can be calculated (Higgins and Thompson, 2002).”
BackgroundMethodInfluentialSelf-citationGelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276
Kass, R. E., & Raftery, A. E. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476572 · Cited by 12,558
Wasserman, S. S., Hedges, L. V., & Olkin, I. (1988) · Journal of Educational Statistics · doi:10.2307/1164953 · Cited by 10,377
Statistical Methods for Meta-Analysis
Rosenbaum, P. R., Hedges, L., & Olkin, I. (1987) · Journal of the American Statistical Association · doi:10.2307/2289186 · Cited by 6,027 · cited 1×
“A common misinterpretation of the random-effects assumption is that the studies themselves are sampled from a population of studies (Hedges, 1987; Anello and Fleiss, 1995; Colditz et al., 1995).”
BackgroundStatistical Methods for Meta-Analysis.
Freeman, P. R., Hedges, L. V., & Olkin, I. (1986) · Biometrics · doi:10.2307/2531069 · Cited by 4,840
Gelman, A. (2006) · Bayesian Analysis · doi:10.1214/06-ba117a · Cited by 4,050 · cited 1×
“It has been suggested that a prior distribution on τ might comprise the positive part of a symmetric distribution around 0, say Cauchy or normal (Gelman, 2006).”
BackgroundAssessing the quality of controlled clinical trials
Jüni, P., Altman, D. G., & Egger, M. (2001) · BMJ · doi:10.1136/bmj.323.7303.42 · Cited by 3,309 · cited 1×
“There are strong arguments against the former (Greenland and O’Rourke, 2001) and an item-based approach to dealing with quality is to be preferred (Jüni et al., 2001).”
Background
Research works printed but not linked: 3
- DuMouchel, 1994, Hierarchical Bayes linear models for meta-analysis
- Morris, 1992, Hierachical models for combining information and for meta-analysis, Bayes. Statist., 4, 321
- Stein, 1956, Proc. 3rd Berkeley Symp, 197
Cited by
Sorted by citations
Items 301–400 of 1,013
Beyond the forest plot: The drapery plot
Rücker, G., & Schwarzer, G. (2020) · Research Synthesis Methods · doi:10.1002/jrsm.1410 · Cited by 123
“It is recommended to add a prediction interval, which gives a region where the estimate from a single future study is expected, based on the random effects model.(19) In this paper we propose a drapery plot as a complementary figure to a forest plot.”
BackgroundKrieglstein, F., Beege, M., Rey, G. D., Ginns, P., Krell, M., & Schneider, S. (2022) · Educational Psychology Review · doi:10.1007/s10648-022-09683-4 · Cited by 167
“On the assumption that reliability estimates represent different populations, a random-effects model was preferred to a fixed-effects model for the meta-analysis (Higgins et al., 2009).”
MethodThe role of impulsivity in pediatric obesity and weight status: A meta-analytic review
Thamotharan, S., Lange, K. L., Zale, E. L., Huffhines, L. P., & Fields, S. A. (2012) · Clinical Psychology Review · doi:10.1016/j.cpr.2012.12.001 · Cited by 119
The epidemiology of hepatitis C virus in Iran: Systematic review and meta-analyses
Mahmud, S., Akbarzadeh, V., & Abu-Raddad, L. J. (2018) · Scientific Reports · doi:10.1038/s41598-017-18296-9 · Cited by 123
Teo, A. K. J., Singh, S. R., Prem, K., Hsu, L. Y., & Yi, S. (2021) · Respiratory Research · doi:10.1186/s12931-021-01841-6 · Cited by 136
“We incorporated heterogeneity into random-effects models using the Bayesian approach [23], which could yield more accurate interval estimates than conventional methods, especially for studies with a small Fig.”
MethodGraybill, L. A., Kasaro, M. P., Freeborn, K., Walker, J. S., Poole, C., Powers, K. A., Mollan, K. R., Rosenberg, N. E., Vermund, S. H., Mutale, W., et al. (2020) · AIDS · doi:10.1097/qad.0000000000002487 · Cited by 121
Statistical Models and Methods for Network Meta-Analysis
Madden, L. V., Piepho, H., & Paul, P. A. (2016) · Phytopathology · doi:10.1094/phyto-12-15-0342-rvw · Cited by 120
“In meta-analytical model fitting, the residual variances (or Ri) for each study are held fixed (Higgins et al. 2009; Madden and Paul 2011).”
BackgroundInfluentialWorkplace interventions for reducing sitting at work
Shrestha, N., Kukkonen-Harjula, K. T., Verbeek, J. H. A. M., Ijaz, S., Hermans, V., & Pedišić, Ž. (2018) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd010912.pub5 · Cited by 120
Wolf, V., Kühnel, A., Teckentrup, V., Koenig, J., & Kroemer, N. B. (2021) · Psychophysiology · doi:10.1111/psyp.13933 · Cited by 124
Hao, H. Q., Zhang, J. F., He, Q. Q., & Wang, Z. (2019) · Osteoarthritis and Cartilage · doi:10.1016/j.joca.2018.10.009 · Cited by 118
Blöchl, M., Meißner, S., & Nestler, S. (2018) · Journal of Affective Disorders · doi:10.1016/j.jad.2018.12.082 · Cited by 125
Dmochowski, R. R., Thai, S., Iglay, K., Enemchukwu, E., Tee, S., Varano, S., Girman, C. J., Radican, L., Mudd, P. N., & Poole, C. (2020) · Neurourology and Urodynamics · doi:10.1002/nau.24536 · Cited by 122
“Consistency of study results was assessed using homogeneity tests with Cochran's Q statistic(24) and 95% CIs and 95% prediction intervals (PIs) were reported.(25) I(2) was also calculated for reference.”
MethodAlzahrani, A. S., Price, M. J., Greenfield, S., & Paudyal, V. (2021) · European Journal of Clinical Pharmacology · doi:10.1007/s00228-021-03097-x · Cited by 118
Sui, Y., Ettema, D., & Helbich, M. (2022) · Health and Place · doi:10.1016/j.healthplace.2022.102893 · Cited by 108
Can Social Policies Improve Health? A Systematic Review and Meta‐Analysis of 38 Randomized Trials
Courtin, É., Kim, S., SONG, S., Yu, W., & Muennig, P. A. (2020) · Milbank Quarterly · doi:10.1111/1468-0009.12451 · Cited by 117
Phillips, R. S., Friend, A. J., Gibson, F., Houghton, E., Gopaul, S., Craig, J. V., & Pizer, B. L. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007786.pub3 · Cited by 116
Social identification and depression: A meta‐analysis
Postmes, T., Wichmann, L. J., van Valkengoed, A. M., & van der Hoef, H. (2018) · European Journal of Social Psychology · doi:10.1002/ejsp.2508 · Cited by 126
Random‐effects meta‐analysis of few studies involving rare events
Günhan, B. K., Röver, C., & Friede, T. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1370 · Cited by 122
Thompson, S. G., Kaptoge, S., White, I. R., Wood, A., Perry, P., & Danesh, J. (2010) · International Journal of Epidemiology · doi:10.1093/ije/dyq063 · Cited by 110
Self-citationIntroduction to systematic reviews and meta‐analysis
McKenzie, J. E., Beller, E. M., & Forbes, A. B. (2016) · Respirology · doi:10.1111/resp.12783 · Cited by 101
Systematic review of methods for individual patient data meta- analysis with binary outcomes
Thomas, D., Radji, S., & Benedetti, A. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-79 · Cited by 110
“[8, 9] In the context of an AD-MA, this is known as meta-regre ssion and may use study level covariates or aggregated patient level information.”
MethodAvoiding zero between‐study variance estimates in random‐effects meta‐analysis
Chung, Y., Rabe‐Hesketh, S., & Choi, I. (2013) · Statistics in Medicine · doi:10.1002/sim.5821 · Cited by 109
“First, the studies tend to be diverse [3,4], whereas the fixed-effects approach assumes that they are ‘functionally equivalent’ [5, p.”
BackgroundMethodCirocchi, R., D’Andrea, V., Arezzo, A., Abraha, I., Passera, R., Avenia, N., Randolph, J., & Barczyński, M. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd012483 · Cited by 109
The cognitive profile of myotonic dystrophy type 1: A systematic review and meta-analysis
Okkersen, K., Buskes, M. H. M., Groenewoud, J. M. M., Kessels, R. P. C., Knoop, H., van Engelen, B. G. M., & Raaphorst, J. (2017) · Cortex · doi:10.1016/j.cortex.2017.08.008 · Cited by 119
Westwood, S. J., Raduà, J., & Rubia, K. (2021) · Journal of Psychiatry and Neuroscience · doi:10.1503/jpn.190179 · Cited by 114
Meta‐analysis of a binary outcome using individual participant data and aggregate data
Riley, R. D., & Steyerberg, E. W. (2010) · Research Synthesis Methods · doi:10.1002/jrsm.4 · Cited by 108
“Though a random-effects meta-analysis model can account for this heterogeneity, the ‘pooled’ meta-analysis estimate then describes some average of the measure across all included populations, which may not be clinically meaningful [1, 2].”
BackgroundCorrecting for Publication Bias in a Meta-Analysis with the P-uniform* MethodPreprint
van Aert, R. C. M., & van Assen, M. A. L. M. (2018) · doi:10.31222/osf.io/zqjr9 · Cited by 108
Kelley, G. A., Kelley, K. S., & Kohrt, W. M. (2013) · International Journal of Endocrinology · doi:10.1155/2013/741639 · Cited by 120
Potentially Inappropriate Prescribing Among Older Persons: A Meta-Analysis of Observational Studies
Liew, T. M., Lee, C. S., Goh, K. L. S., & Chang, Z. Y. (2019) · The Annals of Family Medicine · doi:10.1370/afm.2373 · Cited by 110
Heterogeneity in meta-analyses: an unavoidable challenge worth exploring
Choi, G. J., & Kang, H. (2025) · Korean Journal of Anesthesiology · doi:10.4097/kja.25001 · Cited by 137
“Statistical heterogeneity provides crucial insights into the consistency and applicability of pooled results, ensuring informed decision making in both research and clinical settings [9,10].”
Kim, J. Y., Lee, K. H., Kang, J., Borcoman, É., Saâda-Bouzid, E., Kronbichler, A., Hong, S. H., Rezende, L. F. M., Ogino, S., Keum, N., et al. (2019) · Cancers · doi:10.3390/cancers11111699 · Cited by 104
“We also estimated the 95% prediction interval, which reflects the variation in effect size over different settings [49].”
BackgroundBasic study design influences the results of orthodontic clinical investigations
Papageorgiou, S. N., Xavier, G. M., & Cobourne, M. T. (2015) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2015.03.008 · Cited by 108
“The 95% uncertainty intervals [similar to confidence interval (CIs)] around the I(2) were calculated [27] using the noncentral c(2) approximation of Q [28]; 95% predictive intervals (PIs) were calculated for the DSMD, which incorporate existing heterogeneity and provide a range of possible effects for a future meta-an…”
MethodTanriver-Ayder, E., Faes, C., de Casteele, T. V., McCann, S., & Macleod, M. R. (2021) · BMJ Open Science · doi:10.1136/bmjos-2020-100074 · Cited by 108
Graham, P. L., & Moran, J. L. (2012) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2011.09.012 · Cited by 105
Association of psoriasis with stroke and myocardial infarction: meta‐analysis of cohort studies
Xu, T., & Zhang, Y. ‐. (2012) · British Journal of Dermatology · doi:10.1111/bjd.12002 · Cited by 105
Combining multiple imputation and meta‐analysis with individual participant data
Burgess, S., White, I. R., Resche‐Rigon, M., & Wood, A. (2013) · Statistics in Medicine · doi:10.1002/sim.5844 · Cited by 105
de Jong, V. M. T., Moons, K. G. M., Riley, R. D., Smith, C. T., Marson, A. G., Eijkemans, M. J. C., & Debray, T. P. A. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1384 · Cited by 104
Moran, J. L., Graham, P. L., Rockliff, S., & Bersten, A. D. (2010) · Critical Care · doi:10.1186/cc9182 · Cited by 105
“The degree of asymmetry of the contour-enhanced funnel plot in the low-dose cohort (see Results, Mortality outcome, above) raises concerns about a random effects methodology [ 69 ], but there was no quantitative evidence of smallstudy effects (at the 0.1 level) and the number of studies was small.”
MethodResultInfluentialEsteves, S., Roque, M., & Agarwal, A. (2015) · Asian Journal of Andrology · doi:10.4103/1008-682x.163269 · Cited by 85
Roshanaei-Moghaddam, B., Pauly, M. C., Atkins, D. C., Baldwin, S. A., Stein, M. B., & Roy-Byrne, P. (2011) · Depression and Anxiety · doi:10.1002/da.20829 · Cited by 102
“Meta-analyses used a random-effects model, which is appropriate when there is notable heterogeneity of effect sizes and also conceptually reflects that the included studies represent a sample from a larger population of studies.[25] We examined therapy versus 561 Review: Relative Effects of CBT and Pharmacotherapy”
MethodWinn, D., Lee, Y., Hashibe, M., Boffetta, P., & the INHANCE consortium (2015) · Oral Diseases · doi:10.1111/odi.12342 · Cited by 102
Kelley, G. A., & Kelley, K. S. (2013) · Journal of Obesity · doi:10.1155/2013/783103 · Cited by 118
“where t is the centile point (95%) of the t distribution with k− 2 degrees of freedom, se(2) is the squared standard error, and τ(2) is the between-study variance [34, 35].”
BackgroundBayesian methods for the design and interpretation of clinical trials in very rare diseases
Hampson, L. V., Whitehead, J., Eleftheriou, D., & Brogan, P. A. (2014) · Statistics in Medicine · doi:10.1002/sim.6225 · Cited by 103
“If, a priori, characteristics of patients recruited into the related and future trials are known to differ systematically in a way that can be predicted, it is not realistic to regard the parameters in the different trials as exchangeable [31] nor to represent their priors as independent and identically distributed.”
Belbasis, L., Bellou, V., & Evangelou, E. (2016) · Neuroepidemiology · doi:10.1159/000443146 · Cited by 82
Belbasis, L., Stefanaki, I., Stratigos, A., & Εvangelou, Ε. (2016) · Journal of Dermatological Science · doi:10.1016/j.jdermsci.2016.09.003 · Cited by 106
Trial sequential analysis: adding a new dimension to meta‐analysis
Shah, A., & Smith, A. F. (2019) · Anaesthesia · doi:10.1111/anae.14705 · Cited by 102
“Trial sequential analysis has previously been described as a hybrid position between frequentist and Bayesian approaches, with the sequential analysis arising from frequentist statistics, and the Bayesian component arising from a single a priori effect estimate of the intervention (although Bayesian analysis incorpora…”
MethodPatikorn, C., Saidoung, P., Pham, T., Phisalprapa, P., Lee, Y. Y., Varady, K. A., Veettil, S. K., & Chaiyakunapruk, N. (2023) · BMC Medicine · doi:10.1186/s12916-023-02874-y · Cited by 101
Wong, J. K., Cauraugh, J. H., Ho, K. W. D., Broderick, M., Ramirez‐Zamora, A., Almeida, L., Shukla, A. W., Wilson, C., de Bie, R. M. A., Weaver, F. M., et al. (2018) · Parkinsonism & Related Disorders · doi:10.1016/j.parkreldis.2018.08.017 · Cited by 101
Masika, G. M., Yu, D. S. F., & Li, P. W. C. (2020) · Journal of Advanced Nursing · doi:10.1111/jan.14362 · Cited by 110
Halasa, T., Nielen, M., Whist, A. C., & Østerås, O. (2009) · Journal of Dairy Science · doi:10.3168/jds.2008-1741 · Cited by 98
Fully Bayesian Hierarchical Modelling in Two Stages, with Application to Meta-Analysis
Lunn, D. J., Barrett, J., Sweeting, M. J., & Thompson, S. G. (2013) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12007 · Cited by 98
“At the second stage, the estimates are combined across studies; in a random-effects meta-analysis, potential heterogeneity between the study-specific parameters is permitted (Higgins et al., 2009).”
BackgroundSelf-citationRiley, R. D., Kauser, I., Bland, M., Thijs, L., Staessen, J. A., Wang, J., Gueyffier, F., & Deeks, J. J. (2013) · Statistics in Medicine · doi:10.1002/sim.5726 · Cited by 100
“This interval shows the potential effect of treatment when it is applied within a randomly selected population that is similar to a population from one of the trials included in the meta-analysis [32, 33].”
ResultHeida, K. Y., Velthuis, B. K., Oudijk, M. A., Reitsma, J. B., Bots, M. L., Franx, A., van Dunné, F. M., & on behalf of the Dutch Guideline Development Group on Cardiovascular Risk Management after Reproductive Disorders (2016) · European Journal of Preventive Cardiology · doi:10.1177/2047487314566758 · Cited by 100
“The amount of between-study variation (the tau-squared estimate of a random effects model) is a key factor determining the width of a 95% prediction interval: large values of between-study variation will result in a large prediction interval, even if a large number of studies is included in a review.(27) Funnel plot a…”
ResultTesting overall and moderator effects in random effects meta‐regression
Huizenga, H. M., Visser, I., & Dolan, C. V. (2010) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711010x522687 · Cited by 103
Meta-analysis in evidence-based healthcare
Doi, S. A. R., Furuya‐Kanamori, L., Thalib, L., & Barendregt, J. J. (2017) · International Journal of Evidence-Based Healthcare · doi:10.1097/xeb.0000000000000125 · Cited by 98
Mohan, B. P., Chandan, S., Jha, L. K., Khan, S. R., Kotagiri, R., Kassab, L. L., Ravikumar, N. P. G., Bhogal, N., Chandan, O. C., Bhat, I., et al. (2019) · Surgical Endoscopy · doi:10.1007/s00464-019-07135-9 · Cited by 104
Homelessness and the use of Emergency Department as a source of healthcare: a systematic review
Vohra, N., Paudyal, V., & Price, M. J. (2022) · International Journal of Emergency Medicine · doi:10.1186/s12245-022-00435-3 · Cited by 104
Kelley, G. A., & Kelley, K. S. (2015) · PLoS ONE · doi:10.1371/journal.pone.0129181 · Cited by 100
“The use of such cannot only help to determine outcome effects in a new study but also may be more valid for decision-making [31].”
BackgroundEvidence Synthesis for Decision Making 7
Ades, A. E., Caldwell, D. M., Reken, S., Welton, N. J., Sutton, A. J., & Dias, S. (2013) · Medical Decision Making · doi:10.1177/0272989x13485156 · Cited by 98
Individual patient data meta-analysis of survival data using Poisson regression models
Crowther, M. J., Riley, R. D., Staessen, J. A., Wang, J., Gueyffier, F., & Lambert, P. C. (2012) · BMC Medical Research Methodology · doi:10.1186/1471-2288-12-34 · Cited by 102
Nj, A., Abudou, M., Candeias, & Wu, T. (2014) · Cited by 100
Dhiman, R. K., Thumburu, K. K., Verma, N., Chopra, M., Rathi, S., Dutta, U., Singal, A. K., Taneja, S., Duseja, A. K., & Singh, M. (2019) · Clinical Gastroenterology and Hepatology · doi:10.1016/j.cgh.2019.08.047 · Cited by 100
Systematic review with meta‐analysis: mortality in acute severe ulcerative colitis
Dong, C., Metzger, M., Holsbø, E., Perduca, V., & Carbonnel, F. (2019) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.15592 · Cited by 102
Molina‐García, P., Mora‐Traverso, M., Prieto‐Moreno, R., Díaz-Vásquez, A., Antony, B., & Ariza‐Vega, P. (2023) · Annals of Physical and Rehabilitation Medicine · doi:10.1016/j.rehab.2023.101791 · Cited by 103
Candidate genes in panic disorder: meta-analyses of 23 common variants in major anxiogenic pathways
Howe, A. S., Buttenschøn, H. N., Bani‐Fatemi, A., Maron, E., Otowa, T., Erhardt, A., Binder, E. B., Gregersen, N. O., Mors, O. N., Woldbye, D. P. D., et al. (2015) · Molecular Psychiatry · doi:10.1038/mp.2015.138 · Cited by 99
Konstantonis, D., Vasileiou, D., Papageorgiou, S. N., & Eliades, T. (2018) · European Journal Of Oral Sciences · doi:10.1111/eos.12409 · Cited by 100
“We calculated 95% CIs around all heterogeneity measures to quantify existing uncertainty, and calculated 95% predictive intervals (PrIs) for meta-analyses of three trials or more, to incorporate existing heterogeneity and provide a clinically relevant range of possible effects for a future clinical setting (32).”
MethodCatecholamines in Post-traumatic Stress Disorder: A Systematic Review and Meta-Analysis
Pan, X., Kaminga, A. C., Wen, S. W., & Liu, A. (2018) · Frontiers in Molecular Neuroscience · doi:10.3389/fnmol.2018.00450 · Cited by 106
“However, the random effect model incorporates the estimate of the between study variance to calculate the pooled SMD, and this estimate is more prone to error when the study included in subgroup analyses were < 2 (Higgins et al., 2009).”
BackgroundMethodIndermuehle, A., Bahl, R., Lansky, A. J., Fröhlich, G., Knapp, G., Timmis, A., & Meier, P. (2013) · Heart · doi:10.1136/heartjnl-2012-302945 · Cited by 97
Risk factors for Streptococcus suis infection: A systematic review and meta-analysis
Rayanakorn, A., Goh, B. H., Lee, L., Khan, T. M., & Saokaew, S. (2018) · Scientific Reports · doi:10.1038/s41598-018-31598-w · Cited by 98
Smith, L., Luchini, C., Demurtas, J., Soysal, P., Stubbs, B., Hamer, M., Nottegar, A., Lawlor, R. T., Sánchez, G. F. L., Firth, J., et al. (2019) · Ageing Research Reviews · doi:10.1016/j.arr.2019.02.003 · Cited by 100
Lee, K. H., Seong, H. J., Kim, G., Jeong, G. H., Kim, J. Y., Park, H., Jung, E., Kronbichler, A., Eisenhut, M., Stubbs, B., et al. (2020) · Advances in Nutrition · doi:10.1093/advances/nmaa055 · Cited by 101
Siddiqi, T. J., Usman, M., Shahid, I., Ahmed, J., Khan, S. U., Ya’qoub, L., Rihal, C. S., & Alkhouli, M. A. (2021) · European Journal of Preventive Cardiology · doi:10.1093/eurjpc/zwab018 · Cited by 102
“We used random effects model to account for any potential statistical heterogeneity.(10) When SEs were not available, they were calculated from the confidence intervals.”
MethodChu, C. D., Chen, M. H., McCulloch, C. E., et al. (2021) · Kidney Medicine · doi:10.1016/j.xkme.2021.03.014 · Cited by 97
Statins and Multiple Noncardiovascular Outcomes
He, Y., Li, X., Gašević, D., Brunt, E., McLachlan, F., Millenson, M. E., Timofeeva, M. N., Ioannidis, J. P. A., Campbell, H. J., & Τheodoratou, E. (2018) · Annals of Internal Medicine · doi:10.7326/m18-0808 · Cited by 97
Himmelreich, J. C. L., Veelers, L., Lucassen, W. A. M., Schnabel, R. B., Rienstra, M., van Weert, H. C. P. M., & Harskamp, R. E. (2020) · EP Europace · doi:10.1093/europace/euaa005 · Cited by 100
“When heterogeneity in meta-analysis of C-statistics was high (I(2) > 30%(18)), we derived a 95% prediction interval (95% PI) using methods described previously.(19) We assessed overall discrimination of models by the summary C-statistic.”
MethodTandon, S., Smith, C. T., Riley, R. D., Boyd, M. T., & Jones, T. M. (2010) · Cancer Epidemiology Biomarkers & Prevention · doi:10.1158/1055-9965.epi-09-0981 · Cited by 95
“In all the other meta-analyses that exhibit heterogeneity, it is clinically and statistically more informative to focus on the estimated 95% prediction interval for the underlying HR in a future study (16); this tells us the range of possible HR values in a new study that chooses its own particular set of study charac…”
BackgroundSi, L., Winzenberg, T. M., de Graaff, B., & Palmer, A. J. (2014) · Osteoporosis International · doi:10.1007/s00198-014-2636-2 · Cited by 100
“HSUVs were weighted by the inverse of variance [27].”
MethodCrowther, M. J., Look, M. P., & Riley, R. D. (2014) · Statistics in Medicine · doi:10.1002/sim.6191 · Cited by 95
Transperitoneal versus retroperitoneal laparoscopic adrenalectomy for adrenal tumours in adults
Arezzo, A., Bullano, A., Cochetti, G. G., Cirocchi, R., Randolph, J., Mearini, E. E., Evangelista, A., Ciccone, G., Bonjer, H. J., & Morino, M. (2018) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd011668.pub2 · Cited by 96
“Higgins 2009 Higgins JPT, Thompson SG, Spiegelhalter DJ.”
MethodHøye, A. K. (2018) · Accident Analysis & Prevention · doi:10.1016/j.aap.2018.08.001 · Cited by 94
Assessing Heterogeneity in Random-Effects Meta-analysis
Langan, D. (2021) · Methods in molecular biology · doi:10.1007/978-1-0716-1566-9_4 · Cited by 99
Huppertz, V., Guida, S., Holdoway, A., Strilciuc, Ș., Baijens, L. W. J., Schols, J. M. G. A., van Helvoort, A., Lansink, M., & Muresanu, D. F. (2022) · Frontiers in Neurology · doi:10.3389/fneur.2021.780080 · Cited by 101
“A RE meta-analysis model was preferred over a FE (29, 30) and used for the interpretation of the results.”
MethodSelenium for preventing cancer
Vinceti, M., Dennert, G., Crespi, C. M., Zwahlen, M., Brinkman, M. T., Zeegers, M. P., Horneber, M., D’Amico, R., & Giovane, C. D. (2014) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd005195.pub3 · Cited by 151
Menges, D., Yebyo, H. G., Sivec-Muniz, S., Haile, S. R., Barbier, M. C., Tomonaga, Y., Schwenkglenks, M. M., & Puhan, M. A. (2022) · European Urology Oncology · doi:10.1016/j.euo.2022.04.007 · Cited by 99
Dealing with clinical heterogeneity in meta‐analysis. Assumptions, methods, interpretation
Kriston, L. (2013) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.1377 · Cited by 94
“…true treatment effect, while random-effects models assume that no single true treatment effect exists, but each trial estimates a trial-specific true treatment effect, with these effects following a certain (commonly normal) distribution (Lau et al., 1998; Higgins et al., 2009; Riley et al., 2011).”
BackgroundShort-acting insulin analogues versus regular human insulin for adults with type 1 diabetes mellitus
Fullerton, B., Siebenhofer, A., Jeitler, K., Horvath, K., Semlitsch, T., Berghold, A., Plank, J., Pieber, T. R., & Gerlach, F. M. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd012161 · Cited by 94
Ori, R., Amos, T., Bergman, H., Soares‐Weiser, K., Ipser, J., & Stein, D. J. (2015) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007803.pub2 · Cited by 104
Kelley, G. A., Kelley, K. S., & Hootman, J. M. (2015) · Arthritis Research & Therapy · doi:10.1186/s13075-015-0533-5 · Cited by 227
“However, PI should not be confused with CI since PI are based on a random mean effect while CI are not [60].”
BackgroundMethodChalkowski, K., Wilson, A. E., Lepczyk, C. A., & Zohdy, S. (2019) · Biology Letters · doi:10.1098/rsbl.2018.0840 · Cited by 99
Papola, D., Ostuzzi, G., Gastaldon, C., Morgano, G. P., Dragioti, E., Carvalho, A. F., Fusar‐Poli, P., Correll, C. U., Solmi, M., & Barbui, C. (2019) · Acta Psychiatrica Scandinavica · doi:10.1111/acps.13066 · Cited by 95
“PIs further account for heterogeneity between studies and specify the uncertainty for the effect that would be expected in a new study examining that same research question (19).”
BackgroundRöver, C., Bender, R., Dias, S., Schmid, C. H., Schmidli, H., Sturtz, S., Weber, S., & Friede, T. (2021) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 89
Systematic reviews and meta-analyses of diagnostic studies: a practical guideline
Sadeghi, R., & Treglia, G. (2016) · Clinical and Translational Imaging · doi:10.1007/s40336-016-0219-2 · Cited by 95
Flodgren, G., Deane, K., Dickinson, H. O., Kirk, S., Alberti, H., Beyer, F. R., Brown, J. G., Penney, T. L., Summerbell, C. D., & Eccles, M. P. (2010) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd000984.pub2 · Cited by 90
Consensus building for interlaboratory studies, key comparisons, and meta-analysis
Koepke, A., Lafarge, T., Possolo, A. M., & Toman, B. (2017) · Metrologia · doi:10.1088/1681-7575/aa6c0e · Cited by 97
Kunutsor, S. K., Mäkikallio, T. H., Seidu, S., de Araújo, C. G. S., Dey, R. S., Blom, A. W., & Laukkanen, J. A. (2019) · European Journal of Epidemiology · doi:10.1007/s10654-019-00579-2 · Cited by 96
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Erren, T. C., Morfeld, P., Foster, F., Reiter, R. J., Groß, J. V., & Westermann, I. K. (2016) · Chronobiology International · doi:10.3109/07420528.2016.1149486 · Cited by 92
“We fitted RE meta-regression models (Higgins et al., 2009; Knapp & Hartung, 2003) by restricted maximum likelihood (Sutton et al., 2000) and calculated exact p-values via 10 000 permutations (Higgins & Thompson, 2004).”
MethodChoi, E. K., Park, H. B., Lee, K. H., Park, J.-W., Eisenhut, M., van der Vliet, H. J., Kim, G., & Shin, J. I. (2017) · Annals of Oncology · doi:10.1093/annonc/mdx819 · Cited by 88
Metadata
- Authors
- Higgins, J. P. T., Thompson, S. G., & Spiegelhalter, D. J.
- Affiliations
- MRC Biostatistics Unit (GB)
- Corresponding author
- Higgins, Julian P. T.
- Venue
- Journal of the Royal Statistical Society Series A: Statistics in Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2008-07-24
- Volume
- 172
- Issue
- 1
- Pages
- 137-159
- ISSN
- 0964-1998 (ISSN-L)
- 1467-985X
- PMC
- PMC2667312
- OpenAlex
- W2108116635
- Semantic Scholar
- b42717775886e436d97964fca187c3248684112e
- Cited by
- 2,569
- References
- 100
- Citations by year
- 2026: 222 · 2025: 197 · 2024: 219 · 2023: 186 · 2022: 208 · 2021: 246 · 2020: 224 · 2019: 160 · 2018: 153 · 2017: 124 · 2016: 128 · 2015: 117 · 2014: 93 · 2013: 96 · 2012: 89
- FWCI
- 38.18
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series A (Statistics in Society) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Explore Bristol Research (publishedVersion)
- Bristol Research (University of Bristol) (submittedVersion)
- Funders
- UK Medical Research Council (U.1052.00.011, U.1052.00.001, U.1052.00.005)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- random-effects meta-analysis, heterogeneity, Bayesian meta-analysis, prediction intervals, nonparametric inference, hypothesis testing, set-shifting, eating disorders, prior sensitivity
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