Flexible Conditional Borrowing Approaches for Leveraging Historical Data in the Bayesian Design of Superiority Trials

In this paper, we consider the Bayesian design of a randomized, double-blind, placebo-controlled superiority clinical trial. To leverage multiple historical datasets to augment the placebo-controlled arm, we develop three conditional borrowing approaches built upon the borrowing-by-parts prior, the hierarchical prior, and the robust mixture prior. The operating characteristics of the conditional borrowing approaches are examined. Extensive simulation studies are carried out to empirically demonstrate the superiority of the conditional borrowing approaches over the unconditional borrowing or no-borrowing approaches in terms of controlling type I error, maintaining good power, having a large "sweet-spot" region, minimizing bias, and reducing the mean-squared error of the posterior estimate of the mean parameter of the placebo-controlled arm. Computational algorithms are also developed for calculating the Bayesian type I error and power as well as the corresponding simulation errors.