Bayesian Adaptive Clinical Trials

Abstract

Bayesian adaptive designs are emerging as popular approach to develop adaptive clinical trials. In this dissertation, I describe the mathematical steps for computing the theoretical optimal adaptive designs in biomarker-integrated trials and in trials with survival outcomes. Section 1 discusses the optimal design in personalized medicine. The optimal design maximizes the expected trial utility given any pre-specified utility function, though the discussion here focuses on maximizing responses within a given patient horizon. This work provides absolute benchmark for the evaluation of trial designs in targeted therapy with binary treatment outcomes. While treatment efficacy can be measured by a short-term binary outcome in many phase II and phase III trials, patients' progression-free survival time is with significant importance in cancer clinical trials. However, it is often difficult to make a design adaptive to survival outcomes because of the long observation time. In Section 2, an optimal adaptive design is developed so that treatment assignment decision for later patients can be made with complete or partial survival outcomes of early patients. The design also maximizes the expected trial utility given any pre-specified utility function that is of clinical importance. In this section, the focus is on maximizing the expected progression-free survival time. Both Sections1 and 2 include examples of comparing adaptive designs, such as the bayesian adaptive randomization and the play-the-winner rule, in terms of the expected trial utility with respect to the best achievable result. In Section 3, a simulation-based p-value is proposed and can be used to conduct frequentist analysis of Bayesian adaptive clinical trials. The optimal Bayesian design is compared to the equal randomization design in terms of the Type I error and the statistical power. With a fixed trial size and Type I error, the power of the equal randomization design depends on the difference in treatment efficacy, meanwhile the power of the optimal Bayesian design also depends on the size of the patient horizon.