Rare events meta-analysis using the Bayesian beta-binomial model

In meta-analyses of rare events, it can be challenging to obtain a reliable estimate of the pooled effect, in particular when the meta-analysis is based on a small number of studies. Recent simulation studies have shown that the beta-binomial model is a promising candidate in this situation, but have thus far only investigated its performance in a frequentist framework. In this study, we aim to make the beta-binomial model for meta-analysis of rare events amenable to Bayesian inference by proposing prior distributions for the effect parameter and investigating the models' robustness to different specifications of priors for the scale parameter. To evaluate the performance of Bayesian beta-binomial models with different priors, we conducted a simulation study with two different data generating models in which we varied the size of the pooled effect, the degree of heterogeneity, the baseline probability, and the sample size. Our results show that while some caution must be exercised when using the Bayesian beta-binomial in meta-analyses with extremely sparse data, the use of a weakly informative prior for the effect parameter is beneficial in terms of mean bias, mean squared error, and coverage. For the scale parameter, half-normal and exponential distributions are identified as candidate priors in meta-analysis of rare events using the Bayesian beta-binomial model.