Abstract
Methods for random‐effects meta‐analysis require an estimate of the between‐study variance, τ 2. The performance of estimators of τ 2 (measured by bias and coverage) affects their usefulness in assessing heterogeneity of study‐level effects and also the performance of related estimators of the overall effect. However, as we show, the performance of the methods varies widely among effect measures. For the effect measures mean difference (MD) and standardized MD (SMD), we use improved effect‐measure‐specific approximations to the expected value of Q for both MD and SMD to introduce two new methods of point estimation of τ 2 for MD (Welch‐type and corrected DerSimonian‐Laird) and one WT interval method. We also introduce one point estimator and one interval estimator for τ 2 in SMD. Extensive simulations compare our methods with four point estimators of τ 2 (the popular methods of DerSimonian‐Laird, restricted maximum likelihood, and Mandel and Paule, and the less‐familiar method of Jackson) and four interval estimators for τ 2 (profile likelihood, Q‐profile, Biggerstaff and Jackson, and Jackson). We also study related point and interval estimators of the overall effect, including an estimator whose weights use only study‐level sample sizes. We provide measure‐specific recommendations from our comprehensive simulation study and discuss an example.
Highlights
Meta-analysis is a statistical methodology for combining estimated effects from several studies in order to assess their heterogeneity and obtain an overall estimate
We study coverage of confidence intervals for τ2 achieved by five methods, comparing our Q-profile methods based on improved approximations to the distribution of Cochran's Q with the Q-profile method of Viechtbauer,[18] profile-likelihood-based intervals, and methods by Biggerstaff and Jackson[19] and Jackson.[12]
Among the confidence-interval methods reviewed by Veroniki et al,[9] our study includes four: profile-likelihood (PL), Q-profile (QP), Biggerstaff and Jackson (BJ), and Jackson (J). (Veroniki et al consider combinations of a point estimator and an interval estimator, and they point out that some combinations are not appropriate, because the interval estimator may yield CIs that do not contain the particular point estimate of the between-studies variance.) We review the details of these methods in Web Appendix B2
Summary
Meta-analysis is a statistical methodology for combining estimated effects from several studies in order to assess their heterogeneity and obtain an overall estimate. (Another approach, which we do not discuss further, allows the studies' true effects to differ without following a distribution.4) The between-studies variance, τ2, has a key role in estimates of the mean of the distribution of random effects; but it is important as a quantitative indication of heterogeneity,[5] especially because the interpretation of the popular I2 measure[6] is problematic.[7,8] In studying estimation for meta-analysis of MD and SMD, we focus first on τ2 and proceed to the overall effect. Mandel and Paule,[11] and restricted maximum likelihood, and the less-familiar method of Jackson.[12] Three of these four methods match moments to the asymptotic distribution of Cochran's Q statistic, and the fourth ignores the randomness of the inverse-variance weights They all may be applicable only for large sample sizes.
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