Estimation in meta‐analyses of mean difference and standardized mean difference

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.