Estimation of heterogeneity variance based on a generalized Q statistic in meta-analysis of log-odds-ratio

For estimation of heterogeneity variance t(2) in meta-analysis of log-odds-ratio, we derive new mean-and median-unbiased point estimators and new interval estimators based on a generalized Q statistic, Q(F), in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of Q, Q(IV). In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add 0.5 to each cell of the 2 x 2 table when one cell contains a zero count; we include a version that always adds 0.5. The results show that: two of the new point estimators and two of the familiar point estimators are almost unbiased when the total sample size n = 250 and the probability in the Control arm (p(iC)) is 0.1, and when n = 100 and p(iC) is 0.2 or 0.5; for 0.1 = t(2) = 1, all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable when p(iC) = 0.1 and another, when p(iC) = 0.2 or p(iC) = 0.5; and lack of balance between left and right coverage errors for small n and/or p(iC) implies that the available approximations for the distributions of Q(IV) and Q(F) are accurate only for larger sample sizes.