Alone, together: On the benefits of Bayesian borrowing in a meta‐analytic setting

historical studies, naturally leads to empirical Bayes meta-analysis. In this paper we calculate the Bayesian BFPs and study the factors that drive them. We prove that simultaneous mean squared error reduction relative to an uninformed model is always achievable through application of this model. Power and sample size calculations for a future RCT, designed to be informed by multiple external RCTs, are also provided. Potential applications include inference on treatment efficacy from independent trials involving either heterogeneous patient populations or different therapies from a common class.