Comparing various Bayesian random-effects models for pooling randomized controlled trials with rare events

The meta-analysis of rare events presents unique methodological challenges owing to the small number of events. Bayesian methods are often used to combine rare events data to inform decision-making, as they can incorporate prior information and handle studies with zero events without the need for continuity corrections. However, the comparative performances of different Bayesian models in pooling rare events data are not well understood. We conducted a simulation to compare the statistical properties of four parameterizations based on the binomial-normal hierarchical model, using two different priors for the treatment effect: weakly informative prior (WIP) and non-informative prior (NIP), pooling randomized controlled trials with rare events using the odds ratio metric. We also considered the beta-binomial model proposed by Kuss and the random intercept and slope generalized linear mixed models. The simulation scenarios varied based on the treatment effect, sample size ratio between the treatment and control arms, and level of heterogeneity. Performance was evaluated using median bias, root mean square error, median width of 95% credible or confidence intervals, coverage, Type I error, and empirical power. Two reviews are used to illustrate these methods. The results demonstrate that the WIP outperforms the NIP within the same model structure. Among the compared models, the model that included the treatment effect parameter in the risk model for the control arm did not perform well. Our findings confirm that rare events meta-analysis faces the challenge of being underpowered, highlighting the importance of reporting the power of results in empirical studies.