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

For estimation of heterogeneity variance τ 2 $$ {\tau}^2 $$ 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 $$ Q $$ statistic, Q F $$ {Q}_F $$ , 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 $$ Q $$ , Q IV . $$ {Q}_{IV}. $$ 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 $$ 0.5 $$ to each cell of the 2 × 2 $$ 2\times 2 $$ table when one cell contains a zero count; we include a version that always adds 0.5 $$ 0.5 $$ . 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 $$ n\ge 250 $$ and the probability in the Control arm ( p iC $$ {p}_{iC} $$ ) is 0.1, and when n ≥ 100 $$ n\ge 100 $$ and p iC $$ {p}_{iC} $$ is 0.2 or 0.5; for 0.1 ≤ τ 2 ≤ 1 $$ 0.1\le {\tau}^2\le 1 $$ , 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 $$ {p}_{iC}=0.1 $$ and another, when p iC = 0.2 $$ {p}_{iC}=0.2 $$ or p iC = 0.5 $$ {p}_{iC}=0.5 $$ ; and lack of balance between left and right coverage errors for small n $$ n $$ and/or p iC $$ {p}_{iC} $$ implies that the available approximations for the distributions of Q IV $$ {Q}_{IV} $$ and Q F $$ {Q}_F $$ are accurate only for larger sample sizes.