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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).”
BackgroundHow should meta‐regression analyses be undertaken and interpreted?
Thompson, S. G., & Higgins, J. P. T. (2002) · Statistics in Medicine · doi:10.1002/sim.1187 · Cited by 3,026 · cited 2×
“, 2002) and theoretically (Thompson and Higgins, 2002).”
BackgroundSelf-citationKendall's Advanced Theory of Statistics.
Aa, Stuart, A., & Ord, K. (1995) · Journal of the American Statistical Association · doi:10.2307/2291187 · Cited by 2,663
Random-effects model for meta-analysis of clinical trials: An update
DerSimonian, R., & Kacker, R. (2007) · Contemporary Clinical Trials · doi:10.1016/j.cct.2006.04.004 · Cited by 2,374 · cited 2×
“Heterogeneity Several estimators of the heterogeneity variance 72 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).”
MethodBernardo, J. M., & Smith, A. F. M. (1994) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316870 · Cited by 2,178
Prior distributions for variance parameters in hierarchical modelsPreprint
Gelman, A. (2004) · RePEc: Research Papers in Economics · Cited by 1,558
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448
Cochrane Injuries Group Albumin ReviewersWhy albumin may not work
Berger, A. (1998) · BMJ · doi:10.1136/bmj.317.7153.235 · Cited by 1,080
Systematic Review: Why sources of heterogeneity in meta-analysis should be investigated
Thompson, S. G. (1994) · BMJ · doi:10.1136/bmj.309.6965.1351 · Cited by 1,017 · cited 2×
“Keywords: Meta-analysis; Prediction; Random-effects models; Systematic reviews”
BackgroundWinBUGS user manual version 1.4
Spiegelhalter, D. J. (2003) · Medical Entomology and Zoology · Cited by 983
Self-citationMuch ado about nothing: a comparison of the performance of meta-analytical methods with rare events
Bradburn, M. J., Deeks, J. J., Berlin, J. A., & Russell Localio, A. (2007) · Statistics in Medicine · doi:10.1002/sim.2528 · Cited by 938
Toward Evidence-Based Medical Statistics. 2: The Bayes Factor
Goodman, S. N. (1999) · Annals of Internal Medicine · doi:10.7326/0003-4819-130-12-199906150-00019 · Cited by 913
A random‐effects regression model for meta‐analysis
Berkey, C. S., Hoaglin, D. C., Mosteller, F. C., & Colditz, G. A. (1995) · Statistics in Medicine · doi:10.1002/sim.4780140406 · Cited by 896 · cited 1×
“Several researchers have investigated the distribution of the Wald statistic T = μ̂=ŜE.μ̂/, with suggestions to use tk−4 (Berkey et al., 1995), tk−2 (Raghunathan and Ii, 1993) or tk−1 (Follmann and Proschan, 1999), or to use a modified Wald statistic with a tk−1-distribution (Hartung and Knapp,…”
MethodThe Interpretation of Random-Effects Meta-Analysis in Decision Models
Ades, A. E., Lu, G., & Higgins, J. P. T. (2005) · Medical Decision Making · doi:10.1177/0272989x05282643 · Cited by 862 · cited 1×
“This may be the parameter of primary interest: for example, the average efficacy of a treatment may be the most relevant parameter for health care providers (Feinstein, 1995; Light, 1987; Ades et al., 2005).”
BackgroundSelf-citationMeta‐Analysis Of Controlled Clinical Trials
Whitehead, A. (2002) · doi:10.1002/0470854200 · Cited by 827
A refined method for the meta-analysis of controlled clinical trials with binary outcome
Hartung, J., & Knapp, G. (2001) · Statistics in Medicine · doi:10.1002/sim.1009 · Cited by 775 · cited 1×
“…researchers have investigated the distribution of the Wald statistic T = μ̂=ŜE.μ̂/, with suggestions to use tk−4 (Berkey et al., 1995), tk−2 (Raghunathan and Ii, 1993) or tk−1 (Follmann and Proschan, 1999), or to use a modified Wald statistic with a tk−1-distribution (Hartung and Knapp, 2001a, b).”
MethodHiggins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2002) · Journal of Health Services Research & Policy · doi:10.1258/1355819021927674 · Cited by 755 · cited 1×
“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).”
BackgroundSelf-citationNonparametric maximum likelihood estimation of a mixing distribution
Laird, N. (1978) · Journal of the American Statistical Association · doi:10.1080/01621459.1978.10480103 · Cited by 753 · cited 1×
“NPML procedures provide a discrete distribution that is based on a finite number of mass points (Laird, 1978; B6hning, 2005).”
BackgroundA general parametric approach to the meta‐analysis of randomized clinical trials
Whitehead, A., & Whitehead, J. (1991) · Statistics in Medicine · doi:10.1002/sim.4780101105 · Cited by 749 · cited 2×
“A typical classical approach to random-effects meta-analysis (Whitehead and Whitehead, 1991; DerSimonian and Laird, 1986) takes as an estimate of μ the weighted average μ̂=Σ θ̂iω̂i=Σ ω̂i, where ‘inverse variance’ weights are ω̂i = .σ̂2i + τ̂2/−1.”
Encyclopedia of Biostatistics.
Kemp, C. D., Armitage, P., & Coulton, T. (1998) · Biometrics · doi:10.2307/2533871 · Cited by 676
Testing for Qualitative Interactions between Treatment Effects and Patient Subsets
Gail, M., & Simon, R. (1985) · Biometrics · doi:10.2307/2530862 · Cited by 651 · cited 4×
“…been developed (Gail and Simon, 1985; Piantadosi and Gail, 1993; Pan and Wolfe, 1997), addressing a null hypothesis: H0 :{θi < 0 ∀i} or {θi > 0 ∀i}: Gail and Simon (1985) described the use of a test statistic QÅ =min{∑ θ̂2i σ̂−2i I+i , ∑ θ̂2i σ̂−2i I−i }, .9/ where I+i =1 if θ̂i >0 and I+i =0…”
MethodInfluentialIncorporating variations in the quality of individual randomized trials into meta-analysis
Detsky, A. S., Naylor, C. D., O'Rourke, K., McGeer, A. J., & L'Abbé, K. A. (1992) · Journal of Clinical Epidemiology · doi:10.1016/0895-4356(92)90085-2 · Cited by 640 · cited 1×
“An alternative is a quasi-likelihood approach in which the meta-analysis is performed under a common effect assumption .τ2 =0/ and the standard error of the estimate inflated to account for heterogeneity (Detsky et al., 1992).”
MethodBayesian approaches to random-effects meta-analysis: a comparative study
Smith, T. C., Spiegelhalter, D. J., & Thomas, A. (1995) · Statistics in Medicine · doi:10.1002/sim.4780142408 · Cited by 568 · cited 11×
“Within a Bayesian framework using MCMC methods, a predictive distribution for the effect in a new study is available by sampling such a new study, θnew ∼N.μ, τ2/ (Smith et al., 1995).”
BackgroundMethodInfluentialBORROWING STRENGTH FROM EXTERNAL TRIALS IN A META-ANALYSIS
Higgins, J. P. T., & WHITEHEAD, A. (1996) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19961230)15:24 · Cited by 559
Self-citationOn tests of the overall treatment effect in meta-analysis with normally distributed responses
Hartung, J., & Knapp, G. (2001) · Statistics in Medicine · doi:10.1002/sim.791 · Cited by 543 · cited 1×
“…researchers have investigated the distribution of the Wald statistic T = μ̂=ŜE.μ̂/, with suggestions to use tk−4 (Berkey et al., 1995), tk−2 (Raghunathan and Ii, 1993) or tk−1 (Follmann and Proschan, 1999), or to use a modified Wald statistic with a tk−1-distribution (Hartung and Knapp, 2001a, b).”
MethodA systematic review and meta-analysis of set-shifting ability in eating disorders
Roberts, M., Tchanturia, K., Stahl, D. R., Southgate, L., & Treasure, J. L. (2007) · Psychological Medicine · doi:10.1017/s0033291707009877 · Cited by 536 · cited 1×
“Effect sizes, calculated as standardized differences in means, taken from a systematic review of the topic are reproduced in Table 1 (Roberts et al., 2007).”
MethodA LIKELIHOOD APPROACH TO META-ANALYSIS WITH RANDOM EFFECTS
Hardy, R., & Thompson, S. G. (1996) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19960330)15:6 · Cited by 522
Self-citationEncyclopedia of statistical sciences
(2006) · Choice Reviews Online · doi:10.5860/choice.43-6253 · Cited by 521
Lambert, P. C., Sutton, A. J., Burton, P. R., Abrams, K. R., & Jones, D. R. (2005) · Statistics in Medicine · doi:10.1002/sim.2112 · Cited by 511 · cited 1×
“The choice of prior distribution, even among those that are intended to be non-informative, can have substantial effects on the results of the analysis (Lambert et al., 2005).”
BackgroundMultiple-bias modelling for analysis of observational data
Greenland, S. (2005) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2004.00349.x · Cited by 497 · cited 1×
“Alternative approaches to dealing with specific sources of bias are available (Eddy et al., 1992; Greenland, 2005).”
BackgroundPeto, R. (1987) · Statistics in Medicine · doi:10.1002/sim.4780060306 · Cited by 409 · cited 2×
“…aspects, and so on, are randomly selected from a distribution of possibilities, which is an inappropriate interpretation because studies are individually designed dependent on the results of previous studies (Peto, 1987) and the evolutionary process of scientific research (Colditz et al., 1995).”
BackgroundResultConfidence intervals for the amount of heterogeneity in meta‐analysis
Viechtbauer, W. (2006) · Statistics in Medicine · doi:10.1002/sim.2514 · Cited by 399 · cited 3×
“Some methods allow quantification of uncertainty in the estimate, including a full likelihood approach to the meta-analysis (Hardy and Thompson, 1996), and a method based on a x2-distribution for a random-effects version of the Q-statistic (Viechtbauer, 2007; Knapp et al., 2006); Viechtbauer (2007) reviewed several me…”
MethodA General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models
Aitkin, M. A. (1999) · Biometrics · doi:10.1111/j.0006-341x.1999.00117.x · Cited by 393
Greenland, S. (2001) · Biostatistics · doi:10.1093/biostatistics/2.4.463 · Cited by 359
Meta-analysis: Statistical alchemy for the 21st century
Feinstein, A. R. (1995) · Journal of Clinical Epidemiology · doi:10.1016/0895-4356(94)00110-c · Cited by 335 · cited 1×
“This may be the parameter of primary interest: for example, the average efficacy of a treatment may be the most relevant parameter for health care providers (Feinstein, 1995; Light, 1987; Ades et al., 2005).”
BackgroundA bivariate approach to meta-analysis
Van Houwelingen, H. C., Zwinderman, K. H., & Stijnen, T. (1993) · Statistics in Medicine · doi:10.1002/sim.4780122405 · Cited by 327 · cited 2×
“However, NPML has been noted to be unstable (Van Houwelingen et al., 1993) and has not been widely adopted.”
BackgroundBias Modelling in Evidence Synthesis
Turner, R., Spiegelhalter, D. J., Smith, G. C. S., & Thompson, S. G. (2008) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2008.00547.x · Cited by 319
Self-citationEmpirical bayes meta-analysis.
Raudenbush, S. W., & Bryk, A. S. (1985) · Journal of Educational Statistics · doi:10.3102/10769986010002075 · Cited by 299 · cited 2×
“Metaanalytic implementations have made use of the EM algorithm and bootstrapping (Raudenbush and Bryk, 1985; Laird and Louis, 1989).”
BackgroundMethodWarn, D. E., Thompson, S. G., & Spiegelhalter, D. J. (2002) · Statistics in Medicine · doi:10.1002/sim.1189 · Cited by 277 · cited 1×
“For example, when 2×2 contingency tables are available for binary outcomes, metaanalyses are appropriately performed by using binomial likelihoods (Smith et al., 1995; Warn et al., 2002).”
MethodSelf-citationINCORPORATING VARIABILITY IN ESTIMATES OF HETEROGENEITY IN THE RANDOM EFFECTS MODEL IN META-ANALYSIS
Biggerstaff, B. J., & Tweedie, R. L. (1997) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19970415)16:7 · Cited by 272
Heterogeneity in Meta-analysis of Data from Epidemiologic Studies: A Commentary
Colditz, G. A., Burdick, E., & Mosteller, F. (1995) · American Journal of Epidemiology · doi:10.1093/oxfordjournals.aje.a117644 · Cited by 245 · cited 2×
“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).”
BackgroundResultSpiegelhalter, D. J., & Best, N. G. (2003) · Statistics in Medicine · doi:10.1002/sim.1586 · Cited by 236 · cited 1×
“The following approach, which was described by Spiegelhalter and Best (2003), might help to separate heterogeneity due to biases from heterogeneity due to diversity.”
MethodSelf-citationComputer-Assisted Analysis of Mixtures and Applications: Meta-Analysis, Disease Mapping, and Others
Böhning, D. (1999) · Medical Entomology and Zoology · Cited by 220
Meta-Analysis in Medicine and Health Policy
Stangl, D. K. (2000) · CRC Press eBooks · doi:10.1201/9780203909935 · Cited by 213
Investigating causes of heterogeneity in systematic reviews
Glasziou, P., & Sanders, S. (2002) · Statistics in Medicine · doi:10.1002/sim.1183 · Cited by 213 · cited 2×
“) and bias (variation in the quality of the design and conduct of the studies) (Glasziou and Sanders, 2002; Greenland and O’Rourke, 2001).”
BackgroundSome Thoughts on Empirical Bayes Estimation
Robbins, H. E. (1983) · The Annals of Statistics · doi:10.1214/aos/1176346239 · Cited by 182 · cited 1×
“In particular, for the case of all estimates having the same (known) sampling error (σ21 = . . . =σ2k =σ2, say), and with τ2 known, then the linear function of yi that minimizes the expected mean-squared error is (Robbins, 1983) θ̃i =λμ̂+ .1−λ/θ̂i, where λ=σ2=.σ2 + τ2/.”
Ohlssen, D. I., Sharples, L. D., & Spiegelhalter, D. J. (2006) · Statistics in Medicine · doi:10.1002/sim.2666 · Cited by 164
Self-citationA comparison of the power of two tests for qualitative interactions
Piantadosi, S., & Gail, M. H. (1993) · Statistics in Medicine · doi:10.1002/sim.4780121305 · Cited by 153 · cited 2×
“Such tests have been developed (Gail and Simon, 1985; Piantadosi and Gail, 1993; Pan and Wolfe, 1997), addressing a null hypothesis: H0 :{θi < 0 ∀i} or {θi > 0 ∀i}: Gail and Simon (1985) described the use of a test statistic QÅ =min{∑ θ̂2i σ̂−2i I+i , ∑ θ̂2i σ̂−2i I−i }, .9/ where I+i =1 if θ̂i >0…”
BackgroundBayesian Measures of Model Complexity and Fit
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00353 · Cited by 151 · cited 1×
“The deviance information criterion provides an alternative criterion, which is analogous to Akaike’s criterion, which does not require proper prior distributions (Spiegelhalter et al., 2002).”
MethodFlexible parametric models for random‐effects distributions
Lee, K. J., & Thompson, S. G. (2007) · Statistics in Medicine · doi:10.1002/sim.2897 · Cited by 148 · cited 1×
“For example, a t-distribution or skewed distribution might be used to reduce the effect of outlying studies (Smith et al., 1995; Lee and Thompson, 2007), and mixture distributions have been advocated to account for studies belonging to unknown groupings (Bdhning, 2000).”
BackgroundSelf-citationModels for Potentially Biased Evidence in Meta-Analysis using Empirically Based Priors
Welton, N. J., Ades, A. E., Carlin, J. B., Altman, D. G., & Sterne, J. A. C. (2008) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2008.00548.x · Cited by 147
Meta-analysis by the confidence profile method
Eddy, D. M. (1992) · Cited by 144
Computer-Assisted Analysis of Mixtures and Applications
Böhning, D. (2000) · Technometrics · doi:10.1080/00401706.2000.10485740 · Cited by 130 · cited 1×
“For example, a t-distribution or skewed distribution might be used to reduce the effect of outlying studies (Smith et al., 1995; Lee and Thompson, 2007), and mixture distributions have been advocated to account for studies belonging to unknown groupings (Böhning, 2000).”
BackgroundValid Inference in Random Effects Meta‐Analysis
Follmann, D. A., & Proschan, M. A. (1999) · Biometrics · doi:10.1111/j.0006-341x.1999.00732.x · Cited by 128 · cited 1×
“…researchers have investigated the distribution of the Wald statistic T = μ̂=ŜE.μ̂/, with suggestions to use tk−4 (Berkey et al., 1995), tk−2 (Raghunathan and Ii, 1993) or tk−1 (Follmann and Proschan, 1999), or to use a modified Wald statistic with a tk−1-distribution (Hartung and Knapp, 2001a, b).”
MethodInter‐study differences: How should they influence the interpretation and analysis of results?
Bailey, K. R. (1987) · Statistics in Medicine · doi:10.1002/sim.4780060327 · Cited by 108 · cited 1×
“Extensive discussions of meta-analytic tests, particularly relating to common effect analyses, appear elsewhere (Hedges and Olkin, 1985; Bailey, 1987; Thompson, 1998).”
BackgroundKendall's advanced theory of statistics. Vol.2B: Bayesian inference
O’Hagan, A., & Forster, J. J. (2004) · Cited by 99
Exploratory or analytic meta-analysis: Should we distinguish between them?
Anello, C., & Fleiss, J. L. (1995) · Journal of Clinical Epidemiology · doi:10.1016/0895-4356(94)00084-4 · Cited by 95 · 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).”
BackgroundKendall's Advanced Theory of Statistics, Vol. 2B: Bayesian Inference
Ankerst, D. P. (2005) · Journal of the American Statistical Association · doi:10.1198/jasa.2005.s62 · Cited by 92
Assessing the Amount of Heterogeneity in Random‐Effects Meta‐Analysis
Knapp, G., Biggerstaff, B. J., & Hartung, J. G. (2006) · Biometrical Journal · doi:10.1002/bimj.200510175 · Cited by 84 · cited 1×
“…of uncertainty in the estimate, including a full likelihood approach to the meta-analysis (Hardy and Thompson, 1996), and a method based on a χ2-distribution for a random-effects version of the Q-statistic (Viechtbauer, 2007; Knapp et al., 2006); Viechtbauer (2007) reviewed several methods.”
MethodStatistical Methodology in the Pharmaceutical Sciences
Ziegel, E. R. (1991) · Technometrics · doi:10.1080/00401706.1991.10484820 · Cited by 81
A Bayesian Semiparametric Model for Random-Effects Meta-Analysis
Burr, D. L., & Doss, H. (2005) · Journal of the American Statistical Association · doi:10.1198/016214504000001024 · Cited by 78 · cited 1×
“Bayesian semiparametric random-effects distributions have been proposed (Burr et al., 2003; Burr and Doss, 2005; Ohlssen et al., 2007) based on Dirichlet process priors.”
MethodBurr, D. L., Doss, H., Cooke, G. E., & Goldschmidt‐Clermont, P. J. (2003) · Statistics in Medicine · doi:10.1002/sim.1375 · Cited by 70 · cited 1×
“Bayesian semiparametric random-effects distributions have been proposed (Burr et al., 2003; Burr and Doss, 2005; Ohlssen et al., 2007) based on Dirichlet process priors.”
MethodVangel, M. G., & Rukhin, A. L. (1999) · Biometrics · doi:10.1111/j.0006-341x.1999.00129.x · Cited by 67 · cited 1×
“Better, likelihood-based approaches may be used that incorporate uncertainty in the estimation of τ2 (Hardy and Thompson, 1996; Vangel and Rukhin, 1999).”
MethodHierarchical models for multicentre binary response studies
Skene, A. M., & Wakefield, J. C. (1990) · Statistics in Medicine · doi:10.1002/sim.4780090808 · Cited by 64 · cited 1×
“Exchangeability represents a judgement that the treatment effects may be nonidentical but their magnitudes cannot be differentiated a priori (Skene and Wakefield, 1990; Gelman et al., 1995).”
BackgroundKendall's Advanced Theory of Statistics: Vol. 2B, Bayesian Inference.
Dickey, J., & O’Hagan, A. (1996) · Journal of the American Statistical Association · doi:10.2307/2291686 · Cited by 63
Using empirical bayes methods in biopharmaceutical research
Louis, T. A. (1991) · Statistics in Medicine · doi:10.1002/sim.4780100604 · Cited by 54 · cited 2×
“These expressions can be improved on to account for uncertainty in 2 and #2 (Louis, 1991; Morris and Normand, 1992).”
BackgroundMeta‐Analysis of Clinical Trials
Thompson, S. G. (2005) · Encyclopedia of Biostatistics · doi:10.1002/0470011815.b2a01034 · Cited by 52
Self-citationWelton, N. J., Ades, A. E., Caldwell, D. M., & Peters, T. J. (2008) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/j.1467-985x.2008.00558.x · Cited by 51 · cited 1×
“The parameters underlying the bias distributions could also, in principle, be either subjectively assessed (Turner et al., 2008) or estimated by using analyses of multiple meta-analyses (Welton et al., 2008).”
MethodApproximate Bayesian inference for random effects meta-analysis
Abrams, K. R., & Sansó, B. (1998) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19980130)17:2 · Cited by 50
Accumulating evidence from independent studies: What we can win and what we can lose
Light, R. J. (1987) · Statistics in Medicine · doi:10.1002/sim.4780060304 · Cited by 49 · cited 2×
“These expressions can be improved on to account for uncertainty in 2 and #2 (Louis, 1991; Morris and Normand, 1992). The problem was tackled in particular by Morris (1983). Metaanalytic implementations have made use of the EM algorithm and bootstrapping (Raudenbush and Bryk, 1985; Laird and Louis, 1989).”
BackgroundNonlinear Regression, Quasi Likelihood, and Overdispersion in Generalized Linear Models
Tjur, T. (1998) · The American Statistician · doi:10.1080/00031305.1998.10480567 · Cited by 41 · cited 2×
“For example, for Poisson and logistic models the standard error may be multiplied by j/{ Q/(k - 1)} (Tjur, 1998) which approximates the ratio of standard errors from usual random-effects analysis and common effect analyses (Higgins and Thompson, 2002).”
MethodComputer-modeling and Graphical Strategies for Meta-analysis
DuMouchel, W., & Normand, S. T. (2000) · Chapman & Hall/CRC biostatistics series · doi:10.1201/9780203909935.ch6 · Cited by 38 · cited 2×
“973), and using the shrinkage prior that was advocated by DuMouchel and Normand (2000) produces a prediction interval from -0.”
MethodInfluentialAnalysis of binary data from a multicentre clinical trial
Raghunathan, T. E., & Yoichi (1993) · Biometrika · doi:10.1093/biomet/80.1.127 · Cited by 30
Empirical Bayes Confidence Intervals for a Series of Related Experiments
Laird, N. M., & Louis, T. A. (1989) · Biometrics · doi:10.2307/2531491 · Cited by 29 · cited 1×
“Metaanalytic implementations have made use of the EM algorithm and bootstrapping (Raudenbush and Bryk, 1985; Laird and Louis, 1989).”
MethodEmpirical Bayes Methods in Clinical Trials Meta‐Analysis
Stijnen, T., & van Houwelingen, H. C. (1990) · Biometrical Journal · doi:10.1002/bimj.4710320316 · Cited by 26
Böhning, D. (2005) · PubMed · Cited by 20
Hedges, L. V. (1987) · Statistics in Medicine · doi:10.1002/sim.4780060333 · Cited by 16
Cox, D., & Keogh, R. H. (2015) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat00415.pub2 · Cited by 14
Böhning, D. (2005) · Methods of Information in Medicine · doi:10.1055/s-0038-1633931 · Cited by 14 · cited 1×
“NPML procedures provide a discrete distribution that is based on a finite number of mass points (Laird, 1978; Böhning, 2005).”
BackgroundCommentary on pooling the results of clinical trials
Hedges, L. V. (1987) · Statistics in Medicine · Cited by 10
Modeling and Implementation Issues in Bayesian Meta-Analysis
Pauler, D. K., & Wakefield, J. (2000) · doi:10.1201/9780203909935-16 · Cited by 8
Facilitated analysis of data on drug regimen compliance
de Klerk, E., van der Linden, S., van der Heijde, D. M. F. M., & Urquhart, J. (1997) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19970730)16:14 · Cited by 2
Rose effect and the Euro: The magic is gone
Havránek, T. (2009) · Econstor (Econstor) · Cited by 1
Detecting and describing heterogeneity in meta-analysis
Hardy, R. J., & Thompson, S. G. (1998) · Statistics in Medicine · doi:10.1002/(sici)1097-0258(19980430)17:8
Self-citation
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
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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
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Self-citation
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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