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Keywords: meta-analysis, Bayesian analysis, rare events, regulatory science, rosiglitazone
Meta-analysis is a commonly used statistical technique for combining results from multiple studies. A common issue that we encounter when applying a meta-analysis for extremely rare events is sparsity, leading to zero-event trials that may cause extremely skewed distributions of event frequencies and insufficient statistical power to estimate the effect heterogeneity across studies. Bayesian meta-analysis models are often used to handle such issues due to their flexibility. In addition, we can easily study different model assumptions by employing a wide range of prior specifications. In this work, we compare various Bayesian meta-analysis models under a number of different prior distributions. We consider three meta-analysis models: (1) logistic regression model, (2) arm-based model, and (3) beta hyperprior model, each under two assumptions, common treatment effect (CTE) and heterogeneous treatment effect (HTE). For all models, we consider a wide range of priors (from weakly to strongly informative) for model parameters. For the HTE logistic model, we consider uniform, half-Cauchy, Pareto, and half-normal priors for the between study heterogeneity. For the arm-based model, we consider different Wishart priors for the covariance matrix of random effects. For the beta hyperprior model, we consider noninformative priors, including Jeffreys’ prior and a robust mixture prior for event probabilities. We compare performance of the different models via simulation studies under different degrees of infrequency (or rareness), and then illustrate them using a real meta-analysis data: trials for rosiglitazone on the risks of myocardial infarction and of death from cardiovascular causes.