Simulations for the Q statistic with constant and inverse variance weights for binary effect measures
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Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value (under an incorrect null distribution) is part of several popular estimators of the between-study variance, τ^2. Those applications generally do not account for estimation of the variances in the inverse-variance weights. Importantly, those weights make approximating the distribution of Q (more explicitly, Q_IV) rather complicated. As an alternative, we are investigating a Q statistic, Q_F, whose constant weights use only the studies' effective sample sizes. For log-odds-ratio, log-relative-risk, and risk difference as the measure of effect, we study, by simulation, approximations to distributions of Q_IV and Q_F, as the basis for tests of heterogeneity. Results of our simulations are provided and in 114 A4 Figures, 133 pages in total.
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