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

For estimation of heterogeneity variance $$ in meta-analysis of log-odds-ratio, we derive new mean- and median-unbiased point estimators and new interval estimators based on a generalized $$ statistic, $$ , in which the weights depend on only the studies' effective sample sizes. We compare them with familiar estimators based on the inverse-variance-weights version of $$ , $$ In an extensive simulation, we studied the bias (including median bias) of the point estimators and the coverage (including left and right coverage error) of the confidence intervals. Most estimators add $$ to each cell of the $$ table when one cell contains a zero count; we include a version that always adds $$ . 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 $$ and the probability in the Control arm ( $$ ) is 0.1, and when $$ and $$ is 0.2 or 0.5; for $$ , all estimators have negative bias for small to medium sample sizes, but for larger sample sizes some of the new median-unbiased estimators are almost median-unbiased; choices of interval estimators depend on values of parameters, but one of the new estimators is reasonable when $$ and another, when $$ or $$ ; and lack of balance between left and right coverage errors for small $$ and/or $$ implies that the available approximations for the distributions of $$ and $$ are accurate only for larger sample sizes.