Bayesian Estimation and Testing in Random Effects Meta-analysis of Rare Binary Adverse Events.

Meta-analysis has been widely applied to rare adverse event data because it is very difficult to reliably detect the effect of a treatment on such events in an individual clinical study. However, it is known that standard meta-analysis methods are often biased, especially when the background incidence rate is very low. A recent work by Bhaumik et al. (2012) proposed new moment-based approaches under a natural random effects model, to improve estimation and testing of the treatment effect and the between-study heterogeneity parameter. It has been demonstrated that for rare binary events, their methods have superior performance to commonly-used meta-analysis methods. However, their comparison does not include any Bayesian methods, although Bayesian approaches are a natural and attractive choice under the random-effects model. In this paper, we study a Bayesian hierarchical approach to estimation and testing in meta-analysis of rare binary events using the random effects model in Bhaumik et al. (2012). We develop Bayesian estimators of the treatment effect and the heterogeneity parameter, as well as hypothesis testing methods based on Bayesian model selection procedures. We compare them with the existing methods through simulation. A data example is provided to illustrate the Bayesian approach as well.