Bayesian meta-analysis for rare outcomes

Binary meta-analysis studies with rare outcomes frequently include zero or a small number of observations in study groups, creating a sparsity issue with the data. The corrections applied to eliminate the impact of the zero cell counts introduce a bias to the meta-analysis results and potentially distort the inferences about the treatment effect and heterogeneity among the studies. The boundaries of interval estimates become highly biased due to the sparsity of the data. This study proposes two Bayesian random-effects meta-analysis models based on the beta-binomial model with an arc-sine-square-root transformation. The performance of the models in estimating the treatment effect and the in-between study variance is assessed with an extensive Monte Carlo simulation study, and a frequently referred meta-analysis dataset is revisited. The models provide accurate estimates of treatment effect and heterogeneity parameters without a continuity correction. They provide well-calibrated, narrow interval estimates with sufficient coverage of true treatment effect and in-between study variance. They are robust against zero cell counts, very low event probabilities, and unbalanced, skewed data distributions. Recommendations are given for the practical use of the proposed models, and the required model scripts are provided to implement the models using R software.