Combining Bayesian experimental designs and frequentist data analyses: motivations and examples

Recent developments in experimental designs for clinical trials are stimulated by advances in personalized medicine. Clinical trials today seek to answer several research questions for multiple patient subgroups. Bayesian designs, which enable the use of sound utilities and prior information, can be tailored to these settings. On the other hand, frequentist concepts of data analysis remain pivotal. For example, type I/II error rates are the accepted standards for reporting trial results and are required by regulatory agencies. Bayesian designs are often perceived as incompatible with these established concepts, which hinder widespread clinical applications. We discuss a pragmatic framework for combining Bayesian experimental designs with frequentists analyses. The approach seeks to facilitate a more widespread application of Bayesian experimental designs in clinical trials. We discuss several applications of this framework in different clinical settings, including bridging trials and multi-arm trials in infectious diseases and glioblastoma. We also outline computational algorithms for implementing the proposed approach.