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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
How to perform a meta-analysis with R: a practical tutorial
Balduzzi, S., Rücker, G., & Schwarzer, G. (2019) · Evidence Based Mental Health · doi:10.1136/ebmental-2019-300117 · Cited by 5,827
Salanti, G., Ades, A. E., & Ioannidis, J. P. A. (2011) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2010.03.016 · Cited by 3,766
“Predictive intervals Predictive intervals address the uncertainty in the treatment effect that may be expected in a new study comparing a specific pair of treatments [18].”
BackgroundInterpretation of random effects meta-analyses
Riley, R. D., Higgins, J. P. T., & Deeks, J. J. (2011) · BMJ · doi:10.1136/bmj.d549 · Cited by 2,884
Self-citationWhat Is the Male-to-Female Ratio in Autism Spectrum Disorder? A Systematic Review and Meta-Analysis
Loomes, R., Hull, L., & Mandy, W. P. L. (2017) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2017.03.013 · Cited by 2,804
Chapter 9: Analysing Data and Undertaking Meta-Analyses
Deeks, J. J., Higgins, J. P. T., & Altman, D. G. (2008) · Cited by 2,782
Self-citationGraphical tools for network meta-analysis in STATA
Chaimani, A., Higgins, J. P. T., Mavridis, D., Spyridonos, P., & Salanti, G. (2013) · PLoS ONE · doi:10.1371/journal.pone.0076654 · Cited by 2,473
“and predictive ranking probabilities (the probability that each treatment will be placed in each rank in a future study [39,40]) can be estimated with the suboption predict.”
BackgroundSelf-citationPlea for routinely presenting prediction intervals in meta-analysis.
IntHout, J., Ioannidis, J. P. A., Rovers, M. M., & Goeman, J. J. (2016) · BMJ Open · doi:10.1136/bmjopen-2015-010247 · Cited by 2,264
“effects are to be expected for 95% of similar (exchangeable) studies that might be conducted in the future.(4) Therefore, it is well suited to evaluate the variability of the effect of an intervention over different settings.”
BackgroundAnalysing data and undertaking meta‐analyses
Deeks, J. J., Higgins, J. P., Altman, D. G., & on behalf of the Cochrane Statistical Methods Group (2019) · Cochrane Handbook for Systematic Reviews of Interventions · doi:10.1002/9781119536604.ch10 · Cited by 2,672
Self-citationBasics of meta‐analysis: I 2 is not an absolute measure of heterogeneity
Borenstein, M., Higgins, J. P. T., Hedges, L. V., & Rothstein, H. R. (2017) · Research Synthesis Methods · doi:10.1002/jrsm.1230 · Cited by 1,848
“In any real analysis, these values are estimated with error, and if we want to take account of that error, the appropriate formula (Higgins et al., 2009; Riley et al., 2011) is”
BackgroundInfluentialSelf-citationAnalysing Data and Undertaking Meta‐Analyses
Deeks, J. J., Higgins, J. P., & Altman, D. G. (2008) · Cochrane Handbook for Systematic Reviews of Interventions · doi:10.1002/9780470712184.ch9 · Cited by 1,800
Self-citationWilmot, E. G., Edwardson, C. L., Achana, F. A., Davies, M. J., Gorely, T., Gray, L. J., Khunti, K., Yates, T., & Biddle, S. J. H. (2012) · Diabetologia · doi:10.1007/s00125-012-2677-z · Cited by 1,789
Meta-analysis of individual participant data: rationale, conduct, and reporting
Riley, R. D., Lambert, P. C., & Abo-Zaid, G. (2010) · BMJ · doi:10.1136/bmj.c221 · Cited by 1,701
“The one step and two step individual participant data meta-analyses gave identical results. The pooled treatment effect was estimated at -10.16 (95% CI -12.27 to -8.06), indicating that hypertension treatment reduced systolic blood pressure by, on average, 10.16 mm Hg compared with controls. There was also, however, a…”
ResultInfluentialSalanti, G. (2012) · Research Synthesis Methods · doi:10.1002/jrsm.1037 · Cited by 1,729
“Presentation of the results using predictive intervals (Higgins et al., 2009), although infrequent, best conveys the uncertainty due to heterogeneity (Salanti et al., 2010a).”
BackgroundMethodInfluentialRapsomaniki, E., Timmis, A., George, J., Pujades-Rodriguez, M., Shah, A. D., Denaxas, S., White, I. R., Caulfield, M. J., Deanfield, J. E., Smeeth, L., et al. (2014) · The Lancet · doi:10.1016/s0140-6736(14)60685-1 · Cited by 1,643
Meta‐analysis and Mendelian randomization: A review
Bowden, J., & Holmes, M. V. (2019) · Research Synthesis Methods · doi:10.1002/jrsm.1346 · Cited by 1,683
Evaluating the quality of evidence from a network meta-analysis
Salanti, G., Del Giovane, C., Chaimani, A., Caldwell, D. M., & Higgins, J. P. T. (2014) · PLoS ONE · doi:10.1371/journal.pone.0099682 · Cited by 1,402
“A particularly convenient way to do this is to look at predictive intervals for the effect in a new study of each comparison [14;25;26].”
BackgroundSelf-citationDobbins, M., Husson, H., DeCorby, K., & LaRocca, R. L. (2013) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007651.pub2 · Cited by 1,358
The heterogeneity statistic I2 can be biased in small meta-analyses
von Hippel, P. T. (2015) · BMC Medical Research Methodology · doi:10.1186/s12874-015-0024-z · Cited by 1,229
“Under a random-effects model, by contrast, we assume that the true effects βk in the meta-analysis were drawn at random from a larger population of effects, and we seek to make inferences about that larger population [16].”
MethodA meta-analysis of sex differences in human brain structure
Ruigrok, A. N. V., Salimi-Khorshidi, G., Lai, M.-C., Baron-Cohen, S., Lombardo, M. V., Tait, R. J., & Suckling, J. (2014) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2013.12.004 · Cited by 1,192
Effect of lower sodium intake on health: systematic review and meta-analyses
Aburto, N. J., Ziolkovska, A., Hooper, L., Elliott, P., Cappuccio, F. P., & Meerpohl, J. J. (2013) · BMJ · doi:10.1136/bmj.f1326 · Cited by 1,242
“31 32 We used funnel plots to assess whether there was small study bias.”
BackgroundMethodInfluentialDias, S., Sutton, A. J., Ades, A. E., & Welton, N. J. (2013) · Medical Decision Making · doi:10.1177/0272989x12458724 · Cited by 1,207
Trial Sequential Analysis in systematic reviews with meta-analysis
Wetterslev, J., Jakobsen, J. C., & Gluud, C. N. (2017) · BMC Medical Research Methodology · doi:10.1186/s12874-017-0315-7 · Cited by 1,216
Lane, M. M., Gamage, E., Du, S., Ashtree, D. N., McGuinness, A. J., Gauci, S., Baker, P., Lawrence, M., Rebholz, C. M., Srour, B., et al. (2024) · BMJ · doi:10.1136/bmj-2023-077310 · Cited by 1,153
“31 In an umbrella review, if the 95% prediction intervals exclude the null, it indicates a statistically significant range of effect estimates.”
White, I. R., Barrett, J. K., Jackson, D., & Higgins, J. P. T. (2012) · Research Synthesis Methods · doi:10.1002/jrsm.1045 · Cited by 1,114
“d+bdi, can be compared by instead drawing d b from N d;Vþ Σ̂ (Higgins et al., 2009; Riley et al., 2011).”
BackgroundMethodSelf-citationMethodological issues and advances in biological meta-analysis
Nakagawa, S., & Santos, E. S. A. (2012) · Evolutionary Ecology · doi:10.1007/s10682-012-9555-5 · Cited by 1,032
Conceptual and technical challenges in network meta-analysis
Cipriani, A., Higgins, J. P. T., Geddes, J. R., & Salanti, G. (2013) · Annals of Internal Medicine · doi:10.7326/0003-4819-159-2-201307160-00008 · Cited by 1,072
“Random-effects meta-analysis can be applied (33, 34).”
Self-citationImpact of Intraoperative Stimulation Brain Mapping on Glioma Surgery Outcome: A Meta-Analysis
Hamer, P. C. D. W., Robles, S. G., Zwinderman, A. H., Duffau, H., & Berger, M. S. (2012) · Journal of Clinical Oncology · doi:10.1200/jco.2011.38.4818 · Cited by 1,100
Is psychology suffering from a replication crisis? What does “failure to replicate” really mean?
Maxwell, S. E., Lau, M. Y., & Howard, G. S. (2015) · American Psychologist · doi:10.1037/a0039400 · Cited by 1,102
Commentary: Heterogeneity in meta-analysis should be expected and appropriately quantified
Higgins, J. P. T. (2008) · International Journal of Epidemiology · doi:10.1093/ije/dyn204 · Cited by 995
Self-citationKatsanos, K. H., Spiliοpoulos, S., Kitrou, P. M., Krokidis, M. E., & Karnabatidis, D. (2018) · Journal of the American Heart Association · doi:10.1161/jaha.118.011245 · Cited by 1,031
“Hence, a different, but similar treatment effect was assumed as the basis for the random effects modeling.(58) In addition, different methods of analyses (with or without continuity correction and Bayesian methods) were employed to interrogate potential bias and uncertainty arising from meta-analysis of low event rate…”
MethodPopulation Incidence of Guillain-Barré Syndrome: A Systematic Review and Meta-Analysis
Sejvar, J. J., Baughman, A. L., Wise, M. P., & Morgan, O. W. (2011) · Neuroepidemiology · doi:10.1159/000324710 · Cited by 959
Aburto, N., Hanson, S., Gutiérrez, H., Hooper, L., Elliott, P., & Cappuccio, F. P. (2013) · BMJ · doi:10.1136/bmj.f1378 · Cited by 982
Suurmond, R., van Rhee, H., & Hak, T. (2017) · Research Synthesis Methods · doi:10.1002/jrsm.1260 · Cited by 881
“139 If we assume that all studies provide estimates of different true effects, we must also assume that no single overall effect size can express these different true effects' best.(39) Therefore, the prediction interval accurately embraces the notion of heterogeneity and the dispersion of true effects.”
BackgroundHarbord, R. M., & Higgins, J. P. T. (2008) · The Stata Journal: Promoting communications on statistics and Stata · doi:10.1177/1536867x0800800403 · Cited by 897
Self-citationTurner, R. M., Davey, J., Clarke, M. J., Thompson, S. G., & Higgins, J. P. (2012) · International Journal of Epidemiology · doi:10.1093/ije/dys041 · Cited by 837
Self-citationBarnett, D. W., Barnett, A. H., Nathan, A., Cauwenberg, J. V., & Cerin, E. (2017) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-017-0558-z · Cited by 848
Hadfield, J. D., & Nakagawa, S. (2010) · Journal of Evolutionary Biology · doi:10.1111/j.1420-9101.2009.01915.x · Cited by 829
“This type of assumption has been criticized even in the context of controlled clinical trials (Higgins et al., 2009), and would seem untenable when the data are associated with different species (West & Sheldon, 2002).”
MethodLevin, A. T., Hanage, W. P., Owusu-Boaitey, N., Cochran, K. B., Walsh, S. P., & Meyerowitz-Katz, G. (2020) · European Journal of Epidemiology · doi:10.1007/s10654-020-00698-1 · Cited by 844
Multivariate meta-analysis for non-linear and other multi-parameter associations
Gasparrini, A., Armstrong, B., & Kenward, M. G. (2012) · Statistics in Medicine · doi:10.1002/sim.5471 · Cited by 772
“The theoretical arguments that underpin the definition of this modelling framework closely follow the simple univariate model, recently re-evaluated in detail [26].”
White, I. R. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500403 · Cited by 789
“…ranks. cumulative makes the bar or line graph show cumulative ranks. predict ranks the true effects in a future study with the same covariates, thus allowing for heterogeneity as well as parameter uncertainty, as in the calculation of prediction intervals (Higgins, Thompson, and Spiegelhalter 2009).”
A guide to systematic review and meta-analysis of prognostic factor studies
Riley, R. D., Moons, K. G. M., Snell, K. I. E., Ensor, J., Hooft, L., Altman, D. G., Hayden, J. A., Collins, P. G. S., & Debray, T. P. A. (2019) · BMJ · doi:10.1136/bmj.k4597 · Cited by 771
Barker, T. H., Migliavaca, C. B., Stein, C., Colpani, V., Falavigna, M., Aromataris, E., & Munn, Z. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01381-z · Cited by 738
Risk factors for type 2 diabetes mellitus: An exposure-wide umbrella review of meta-analyses
Bellou, V., Belbasis, L., Tzoulaki, I., & Evangelou, E. (2018) · PLOS ONE · doi:10.1371/journal.pone.0194127 · Cited by 713
Jakobsen, J. C., Wetterslev, J., Winkel, P., Lange, T., & Gluud, C. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-120 · Cited by 704
“However, this use would imply integration of complicated models and software for analysing the review results [24,40,41] and would entail the need for specifying multiple prior distributions, which has its own problems [12,24,40,41].”
BackgroundMethodHan, B., & Eskin, E. (2011) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2011.04.014 · Cited by 680
Belbasis, L., Bellou, V., Εvangelou, Ε., Ioannidis, J. P. A., & Tzoulaki, I. (2015) · The Lancet Neurology · doi:10.1016/s1474-4422(14)70267-4 · Cited by 715
Moja, L., Piatti, A., Pecoraro, V. L., Ricci, C., Virgili, G., Salanti, G., Germagnoli, L., Liberati, A., & Banfi, G. (2012) · PLoS ONE · doi:10.1371/journal.pone.0046175 · Cited by 677
Cerin, E., Nathan, A., Cauwenberg, J. V., Barnett, D. W., & Barnett, A. H. (2017) · International Journal of Behavioral Nutrition and Physical Activity · doi:10.1186/s12966-017-0471-5 · Cited by 645
“In line with methodological recommendations for meta-analyses [44], specific combinations of environmental attributes and AT outcomes examined less than five times were considered to be insufficiently studied.”
BackgroundCrocker, J. C., Ricci‐Cabello, I., Parker, A., Hirst, J. A., Chant, A., Petit-Zeman, S., Evans, D., & Rees, S. (2018) · BMJ · doi:10.1136/bmj.k4738 · Cited by 650
Selenium for preventing cancer
Vinceti, M., Filippini, T., Del Giovane, C., Dennert, G., Zwahlen, M., Brinkman, M., Zeegers, M. P., Horneber, M., D'Amico, R., & Crespi, C. M. (2018) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd005195.pub4 · Cited by 649
Quraishi, M. N., Widlak, M., Bhala, N., Moore, D., Price, M., Sharma, N., & Iqbal, T. H. (2017) · Alimentary Pharmacology & Therapeutics · doi:10.1111/apt.14201 · Cited by 617
Power analysis for random-effects meta-analysis
Jackson, D., & Turner, R. (2017) · Research Synthesis Methods · doi:10.1002/jrsm.1240 · Cited by 619
Quantifying the impact of between-study heterogeneity in multivariate meta-analyses
Jackson, D., White, I. R., & Riley, R. D. (2012) · Statistics in Medicine · doi:10.1002/sim.5453 · Cited by 577
Dray, J., Bowman, J., Campbell, E., Freund, M., Wolfenden, L., Hodder, R. K., McElwaine, K., Tremain, D., Bartlem, K., Bailey, J., et al. (2017) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2017.07.780 · Cited by 566
“Research suggests that the inclusion of 4 or fewer studies in random effects meta-analysis may result in imprecise estimations of between-study variance.(105) Therefore, results in the present review of meta-analyses based on minimal numbers of trials, such as for the outcomes of conduct problems, internalizing proble…”
ResultDoi, S. A. R., Barendregt, J. J., Khan, S., Thalib, L., & Williams, G. M. (2015) · Contemporary Clinical Trials · doi:10.1016/j.cct.2015.05.009 · Cited by 596
“A greater diversity that leads to dissimilarity of effects would not bemeta-analyzed [17].”
BackgroundJuhl, C. B., Christensen, R., Roos, E. M., Zhang, W., & Lund, H. (2013) · Arthritis & Rheumatology · doi:10.1002/art.38290 · Cited by 580
“Prediction intervals encompassing the effect of a future study with 95% certainty were estimated in order to evaluate the quantitative impact of inconsistency according to the method of Higgins et al using the between-study variance 2 and the standard error (14).”
MethodA Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models
Chung, Y., Rabe‐Hesketh, S., Dorie, V., Gelman, A., & Liu, J. (2013) · Psychometrika · doi:10.1007/s11336-013-9328-2 · Cited by 598
What causes psychosis? An umbrella review of risk and protective factors
Radua, J., Ramella‐Cravaro, V., Ioannidis, J. P. A., Reichenberg, A., Phiphopthatsanee, N., Amir, T., Yenn Thoo, H., Oliver, D., Davies, C., Morgan, C., et al. (2018) · World Psychiatry · doi:10.1002/wps.20490 · Cited by 553
Classroom management self-efficacy and burnout: A multivariate meta-analysis
Aloe, A. M., Amo, L. C., & Shanahan, M. E. (2014) · Educational Psychology Review · doi:10.1007/s10648-013-9244-0 · Cited by 560
Burke, D. L., Ensor, J., & Riley, R. D. (2017) · Statistics in Medicine · doi:10.1002/sim.7141 · Cited by 538
Bowden, J., Tierney, J. F., Copas, A. J., & Burdett, S. (2011) · BMC Medical Research Methodology · doi:10.1186/1471-2288-11-41 · Cited by 555
“We note that this does not reflect the state-of-the-art in what can estimated via a random effects meta-analysis; one can for instance also estimate trial level effect parameters (θ + ui), predict the likely effects of future studies and test hypotheses relating to these additional parameters [19].”
BackgroundMethodDietary fiber and health outcomes: an umbrella review of systematic reviews and meta-analyses
Veronese, N., Solmi, M., Caruso, M. G., Giannelli, G., Osella, A. R., Evangelou, E., Maggi, S., Fontana, L., Stubbs, B., & Tzoulaki, I. (2018) · The American Journal of Clinical Nutrition · doi:10.1093/ajcn/nqx082 · Cited by 536
Multivariate meta‐analysis: Potential and promise
Jackson, D., Riley, R., & White, I. R. (2011) · Statistics in Medicine · doi:10.1002/sim.4172 · Cited by 530
“Similarly, it allows a joint prediction region [63] for the true sensitivity and specificity in an individual study setting.”
BackgroundUmer, A., Kelley, G. A., Cottrell, L., Giacobbi, P. R., Innes, K. E., & Lilly, C. L. (2017) · BMC Public Health · doi:10.1186/s12889-017-4691-z · Cited by 563
Meta‐analysis and traditional systematic literature reviews—What, why, when, where, and how?
Paul, J., & Barari, M. M. (2022) · Psychology and Marketing · doi:10.1002/mar.21657 · Cited by 640
NUDT15 polymorphisms alter thiopurine metabolism and hematopoietic toxicity
Moriyama, T., Nishii, R., Pérez-Andreu, V., Yang, W., Antillón‐Klussmann, F., Zhao, X., Lin, T.-N., Hoshitsuki, K., Nersting, J., Kihira, K., et al. (2016) · Nature Genetics · doi:10.1038/ng.3508 · Cited by 478
Malin, G. L., Morris, R. K., & Khan, K. S. (2010) · BMJ · doi:10.1136/bmj.c1471 · Cited by 461
“As the focus of this review was to establish the association between cord pH and adverse outcome rather than the value of cord pH as a prognostic test, we did not calculate other summary statistics (including sensitivity, specificity, and likelihood ratios). We calculated the estimated predictive interval for each met…”
The Association between Time Spent Outdoors and Myopia in Children and Adolescents
Sherwin, J. C., Reacher, M. H., Keogh, R. H., Khawaja, A. P., Mackey, D. A., & Foster, P. J. (2012) · Ophthalmology · doi:10.1016/j.ophtha.2012.04.020 · Cited by 483
Evidence Synthesis for Decision Making 3
Dias, S., Sutton, A. J., Welton, N. J., & Ades, A. E. (2013) · Medical Decision Making · doi:10.1177/0272989x13485157 · Cited by 468
Al-Khudairy, L., Loveman, E., Colquitt, J. L., Mead, E., Johnson, R. E., Fraser, H., Olajide, J., Murphy, M., Velho, R., O’Malley, C. L., et al. (2017) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd012691 · Cited by 472
Random-Effects Meta-analysis of Inconsistent Effects: A Time for Change
Cornell, J. E., Mulrow, C. D., Localio, R., Stack, C. B., Meibohm, A. R., Guallar, E., & Goodman, S. N. (2014) · Annals of Internal Medicine · doi:10.7326/m13-2886 · Cited by 453
Corporate governance and environmental social governance disclosure: A meta‐analytical review
Lagasio, V., & Cucari, N. (2019) · Corporate Social Responsibility and Environmental Management · doi:10.1002/csr.1716 · Cited by 526
Meta-analysis of multiple outcomes: a multilevel approach
Van den Noortgate, W., López-López, J. A., Marín-Martínez, F., & Sánchez-Meca, J. (2015) · Behavior Research Methods · doi:10.3758/s13428-014-0527-2 · Cited by 450
Active versus expectant management for women in the third stage of labour
Begley, C., Gyte, G. M., Devane, D., McGuire, W. L., & Weeks, A. D. (2015) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007412.pub4 · Cited by 448
Sleep problems and work injuries: A systematic review and meta-analysis
Uehli, K., Mehta, A. J., Miedinger, D., Hug, K., Schindler, C., Holsboer‐Trachsler, E., Leuppi, J. D., & Künzli, N. (2013) · Sleep Medicine Reviews · doi:10.1016/j.smrv.2013.01.004 · Cited by 474
Neil‐Sztramko, S., Caldwell, H. A. T., & Dobbins, M. (2021) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007651.pub3 · Cited by 552
Fetal and umbilical Doppler ultrasound in high-risk pregnancies
Alfirević, Ž., Stampalija, T., & Gyte, G. M. (2013) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd007529.pub3 · Cited by 440
Environmental risk factors and Parkinson's disease: An umbrella review of meta-analyses
Bellou, V., Belbasis, L., Tzoulaki, I., Εvangelou, Ε., & Ioannidis, J. P. A. (2015) · Parkinsonism & Related Disorders · doi:10.1016/j.parkreldis.2015.12.008 · Cited by 443
Association of Endometrial Cancer Risk With Postmenopausal Bleeding in Women
Clarke, M. A., Long, B. J., Del Mar Morillo, A., Arbyn, M., Bakkum-Gamez, J. N., & Wentzensen, N. (2018) · JAMA Internal Medicine · doi:10.1001/jamainternmed.2018.2820 · Cited by 426
Guidance on the use of the weight of evidence approach in scientific assessments
Hardy, A., Benford, D., Halldorsson, T. I., Jeger, M. J., Knutsen, H. K., More, S. J., Naegeli, H., Noteborn, H. P. J. M., Ockleford, C., Ricci, A., et al. (2017) · EFSA Journal · doi:10.2903/j.efsa.2017.4971 · Cited by 425
“Linkov et al. (2015) consider that multicriteria decision analysis can be used as a proxy for the Bayesian approach to weight of evidence assessment when model formulation is restricted by data limitations.”
MethodMultivariate Random-effects Meta-regression: Updates to Mvmeta
White, I. R. (2011) · The Stata Journal: Promoting communications on statistics and Stata · doi:10.1177/1536867x1101100206 · Cited by 400
Turner, R. M., Jackson, D., Wei, Y., Thompson, S. G., & Higgins, J. P. T. (2015) · Statistics in Medicine · doi:10.1002/sim.6381 · Cited by 410
“A Bayesian random-effects meta-analysis is advantageous in allowing researchers to incorporate external evidence on the likely extent of between-study heterogeneity in a particular research setting, to reduce the imprecision [3, 4], as well as facilitating prediction of effects in future studies and flexibility in mod…”
BackgroundSelf-citationDavey, J., Turner, R. M., Clarke, M. J., & Higgins, J. P. (2011) · BMC Medical Research Methodology · doi:10.1186/1471-2288-11-160 · Cited by 404
Self-citationRhodes, K. M., Turner, R., & Higgins, J. P. T. (2014) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2014.08.012 · Cited by 398
“Alternatively, we can allow for heterogeneity in a random-effects metaanalysis, estimating the summary effect and the betweenstudy variance [2].”
BackgroundSelf-citationSummarizing historical information on controls in clinical trials
Neuenschwander, B. E., Capkun-Niggli, G., Branson, M., & Spiegelhalter, D. J. (2010) · Clinical Trials · doi:10.1177/1740774509356002 · Cited by 398
Self-citationWorkplace interventions for reducing sitting at work
Shrestha, N., Kukkonen-Harjula, K. T., Verbeek, J. H. A. M., Ijaz, S., Hermans, V., & Bhaumik, S. (2016) · Cochrane Database of Systematic Reviews · doi:10.1002/14651858.cd010912.pub3 · Cited by 403
Li, X., Meng, X., Timofeeva, M. N., Tzoulaki, I., Tsilidis, K. K., Ioannidis, J. P. A., Campbell, H. J., & Τheodoratou, E. (2017) · BMJ · doi:10.1136/bmj.j2376 · Cited by 402
Barbui, C., Purgato, M., Abdulmalik, J., Acarturk, C., Eaton, J., Gastaldon, C., Gureje, O., Hanlon, C., Jordans, M., Lund, C., et al. (2020) · The Lancet Psychiatry · doi:10.1016/s2215-0366(19)30511-5 · Cited by 349
“21 Prediction intervals 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.”
A comparison of treatment effectiveness between clear aligner and fixed appliance therapies
Ke, Y., Zhu, Y., & Zhu, M. (2019) · BMC Oral Health · doi:10.1186/s12903-018-0695-z · Cited by 398
Comprehensive Meta‐Analysis Software
Borenstein, M. (2022) · Wiley eBooks · doi:10.1002/9781119099369.ch27 · Cited by 389
Lawry, S., Samii, C., Hall, R., Leopold, A., Hornby, D., & Mtero, F. (2016) · Journal of Development Effectiveness · doi:10.1080/19439342.2016.1160947 · Cited by 366
Prevalence and outcomes of incidental imaging findings: umbrella review
O’Sullivan, J. W., Muntinga, T., Grigg, S. E., & Ioannidis, J. P. A. (2018) · BMJ · doi:10.1136/bmj.k2387 · Cited by 360
Veroniki, A. A., Cogo, E., Rios, P., Straus, S. E., Finkelstein, Y., Kealey, R., Reynen, E., Soobiah, C., Thavorn, K., Hutton, B., et al. (2017) · BMC Medicine · doi:10.1186/s12916-017-0845-1 · Cited by 339
“For the NMA effect estimates, a 95% predictive interval (PrI) was also presented, capturing the magnitude of τ(2) and presenting the interval within which we would expect the treatment effect of a future study to lie [40, 41].”
Teughels, W., Feres, M., Oud, V., Martín, C., Matesanz, P., & Herrera, D. (2020) · Journal Of Clinical Periodontology · doi:10.1111/jcpe.13264 · Cited by 342
Prevalence of Autism Spectrum Disorder in Preterm Infants: A Meta-analysis
Agrawal, S., Rao, S. C., Bulsara, M. K., & Patole, S. (2018) · PEDIATRICS · doi:10.1542/peds.2018-0134 · Cited by 332
Synthesising quantitative evidence in systematic reviews of complex health interventions
Higgins, J. P. T., López-López, J. A., Becker, B. J., Davies, S. R., Dawson, S., Grimshaw, J. M., McGuinness, L. A., Moore, T. H. M., Rehfuess, E. A., Thomas, J., et al. (2019) · BMJ Global Health · doi:10.1136/bmjgh-2018-000858 · Cited by 322
Self-citationKunutsor, S. K., Whitehouse, M. R., Lenguerrand, E., Blom, A. W., Beswick, A. D., & INFORM Team (2016) · PLoS ONE · doi:10.1371/journal.pone.0151537 · Cited by 336
“We also estimated 95% prediction intervals which are used to determine the degree of heterogeneity, as they provide a region in which about 95% of the true study effects are expected to be found [18, 19].”
MethodMortality in Parkinson's disease: A systematic review and meta‐analysis
Macleod, A. D., Taylor, K. S. M., & Counsell, C. E. (2014) · Movement Disorders · doi:10.1002/mds.25898 · Cited by 328
An extended mixed‐effects framework for meta‐analysis
Sera, F., Armstrong, B., Blangiardo, M., & Gasparrini, A. (2019) · Statistics in Medicine · doi:10.1002/sim.8362 · Cited by 345
“26 The pooled estimate can be derived under fixed-effects or random-effects assumptions, 27,28 with random-effects models incorporating the underlying between-study variation into the weights.”
Visualizing Assumptions and Results in Network Meta-analysis: The Network Graphs Package
Chaimani, A., & Salanti, G. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500402 · Cited by 323
“The extent of uncertainty in the estimated treatment effects in meta-analysis is re-flected not only by the confidence intervals but also by the predictive intervals that incorporate the extent of heterogeneity (Higgins, Thompson, and Spiegelhalter 2009; Riley, Higgins, and Deeks 2011).”
Background
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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