Methods for estimating between-study variance and overall effect in meta-analysis of odds-ratios

In random-effects meta-analysis the between-study variance (τ ²) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating τ ² and the overall effect and produce confidence intervals with below-nominal coverage. An improved approximation to the moments of Cochran's Q statistic, suggested by Kulinskaya and Dollinger (KD), yields new point and interval estimators of τ ² and of the overall log-odds-ratio. Another, simpler approach (SSW) uses weights based only on study-level sample sizes to estimate the overall effect. In extensive simulations we compare our proposed estimators with established point and interval estimators for τ ² and point and interval estimators for the overall log-odds-ratio (including the Hartung-Knapp-Sidik-Jonkman interval). Additional simulations included three estimators based on generalized linear mixed models and the Mantel-Haenszel fixed-effect estimator. Results of our simulations show that no single point estimator of τ ² can be recommended exclusively, but Mandel-Paule and KD provide better choices for small and large numbers of studies, respectively. The KD estimator provides reliable coverage of τ ². Inverse-variance-weighted estimators of the overall effect are substantially biased, as are the Mantel-Haenszel odds ratio and the estimators from the generalized linear mixed models. The SSW estimator of the overall effect and a related confidence interval provide reliable point and interval estimation of the overall log-odds-ratio.