Prior distributions for variance parameters in a sparse-event meta-analysis of a few small trials

In rare diseases, typically only a small number of patients are available for a randomized clinical trial. Nevertheless, it is not uncommon that more than one study is performed to evaluate a (new) treatment. Scarcity of available evidence makes it particularly valuable to pool the data in a meta-analysis. When the primary outcome is binary, the small sample sizes increase the chance of observing zero events. The frequentist random-effects model is known to induce bias and to result in improper interval estimation of the overall treatment effect in a meta-analysis with zero events. Bayesian hierarchical modeling could be a promising alternative. Bayesian models are known for being sensitive to the choice of prior distributions for between-study variance (heterogeneity) in sparse settings. In a rare disease setting, only limited data will be available to base the prior on, therefore, robustness of estimation is desirable. We performed an extensive and diverse simulation study, aiming to provide practitioners with advice on the choice of a sufficiently robust prior distribution shape for the heterogeneity parameter. Our results show that priors that place some concentrated mass on small τ values but do not restrict the density for example, the Uniform(-10, 10) heterogeneity prior on the log(τ² ) scale, show robust 95% coverage combined with less overestimation of the overall treatment effect, across varying degrees of heterogeneity. We illustrate the results with meta-analyzes of a few small trials.