Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability.

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.