Simulations for estimation of heterogeneity variance τ^2 in constant and inverse variance weights meta-analysis of log-odds-ratios
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A number of popular estimators of the between-study variance, τ^2, are based on the Cochran's Q statistic for testing heterogeneity in meta analysis. We introduce new point and interval estimators of τ^2 for log-odds-ratio. These include new DerSimonian-Kacker-type moment estimators based on the first moment of Q_F, the Q statistic with effective-sample-size weights, and novel median-unbiased estimators. We study, by simulation, bias and coverage of these new estimators of τ^2 and, for comparative purposes, bias and coverage of a number of well-known estimators based on the Q statistic with inverse-variance weights, Q_IV, such as the Mandel-Paule, DerSimonian-Laird, and restricted-maximum-likelihood estimators, and an estimator based on the Kulinskaya-Dollinger (2015) improved approximation to Q_IV.
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