An integrative shrinkage estimator for random-effects meta-analysis of rare binary events

Meta-analysis has been a powerful tool for inferring the treatment effect between two experimental conditions from multiple studies of rare binary events. Recently, under a random-effects (RE) model, Bhaumik et al. developed a simple average (SA) estimator and showed that with the continuity correction factor 0.5, the SA estimator was the least biased among a set of commonly used estimators. In this paper, under various RE models that allow for treatment groups with equal and unequal variability (in either direction), we develop an integrative shrinkage (iSHRI) estimator based on the SA estimator, which aims to improve estimation efficiency in terms of mean squared error (MSE) that accounts for the bias-variance tradeoff. Through simulation, we find that iSHRI has better performance in general when compared with existing methods, in terms of bias, MSE, type I error and confidence interval coverage. Data examples of rosiglitazone meta-analysis are provided as well, where iSHRI yields competitive results.