Optimal Bayesian adaptive trials when treatment efficacy depends on biomarkers

type="main" xml:lang="en"> Clinical biomarkers play an important role in precision medicine and are now extensively used in clinical trials, particularly in cancer. A response adaptive trial design enables researchers to use treatment results about earlier patients to aid in treatment decisions of later patients. Optimal adaptive trial designs have been developed without consideration of biomarkers. In this article, we describe the mathematical steps for computing optimal biomarker-integrated adaptive trial designs. These designs maximize the expected trial utility given any pre-specified utility function, though we focus here on maximizing patient responses within a given patient horizon. We describe the performance of the optimal design in different scenarios. We compare it to Bayesian Adaptive Randomization (BAR), which is emerging as a practical approach to develop adaptive trials. The difference in expected utility between BAR and optimal designs is smallest when the biomarker subgroups are highly imbalanced. We also compare BAR, a frequentist play-the-winner rule with integrated biomarkers and a marker-stratified balanced randomization design (BR). We show that, in contrasting two treatments, BR achieves a nearly optimal expected utility when the patient horizon is relatively large. Our work provides novel theoretical solution, as well as an absolute benchmark for the evaluation of trial designs in personalized medicine.