Comparison of Prior Distributions for the Heterogeneity Parameter in a Rare Events Meta-Analysis of a Few Studies

Bayesian meta-analysis is a promising approach for rare events meta-analysis. However, the inference of the overall effect in rare events meta-analysis is sensitive to the choice of prior distribution for the heterogeneity parameter. Therefore, it is crucial to assign a convincing prior specification and ensure that it is both plausible and transparent. Various priors for the heterogeneity parameter have been proposed; however, the comparative performance of alternative prior specifications in rare events meta-analysis is poorly understood. Based on a binomial-normal hierarchical model, we conducted a comprehensive simulation study to compare seven heterogeneity prior specifications for binary outcomes, using the odds ratio as the metric. We compared their performance in terms of coverage, median percentage bias, width of the 95% credible interval, and root mean square error (RMSE). We illustrate the results with two recently published rare events meta-analyses of a few studies. The results show that the half-normal prior (with a scale of 0.5), the prior proposed by Turner et al. for the general healthcare setting (without restriction to a specific type of outcome) and for the adverse event setting perform well when the degree of heterogeneity is not relatively high, yielding smaller bias and shorter interval widths with similar coverage and RMSE in most cases compared to other prior specifications. None of the priors performed better when the heterogeneity between-studies were significantly extreme.