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.

Random-effects meta-analysis of few studies involving rare events.

Meta-analyses of clinical trials targeting rare events face particular challenges when the data lack adequate numbers of events for all treatment arms. Especially when the number of studies is low, standard random-effects meta-analysis methods can lead to serious distortions because of such data sparsity. To overcome this, we suggest the use of weakly informative priors (WIPs) for the treatment effect parameter of a Bayesian meta-analysis model, which may also be seen as a form of penalization. As a data model, we use a binomial-normal hierarchical model (BNHM) that does not require continuity corrections in case of zero counts in one or both arms. We suggest a normal prior for the log-odds ratio with mean 0 and standard deviation 2.82, which is motivated (a) as a symmetric prior centered around unity and constraining the odds ratio within a range from 1/250 to 250 with 95% probability and (b) as consistent with empirically observed effect estimates from a set of 37 773 meta-analyses from the Cochrane Database of Systematic Reviews. In a simulation study with rare events and few studies, our BNHM with a WIP outperformed a Bayesian method without a WIP and a maximum likelihood estimator in terms of smaller bias and shorter interval estimates with similar coverage. Furthermore, the methods are illustrated by a systematic review in immunosuppression of rare safety events following pediatric transplantation. A publicly available R package, MetaStan, is developed to automate a Bayesian implementation of meta-analysis models using WIPs.