Estimation using non-central hypergeometric distributions in combining 2×2 tables

We consider estimation of the overall log odds ratio and the between-study variance or heterogeneity variance from a series of independent 2×2 tables. The estimates are obtained using the conditional distributions of the tables with fixed marginal totals, specifically the non-central hypergeometric distribution, along with an assumed normal distribution of the true study-specific log odds ratios. The method presented differs from the traditional random effects meta-analysis approach for 2×2 tables in two respects. First, it does not assume a normal distribution for the observed within-study log odds ratio statistics; and second, it does not require estimation of the heterogeneity variance as a first step for estimation of the overall log odds ratio. Furthermore, the method directly provides an estimate of the heterogeneity variance and an associated standard error. Several real examples are discussed to illustrate the approach outlined in this paper, and to compare it with other common approaches.