A Globally Calibrated Bayesian Optimal Phase II Design for Adaptive Enrichment Trials

Adaptive enrichment can allow the development of an experimental treatment to continue when its activity is insufficient in an all-comer population but remains promising in a prespecified biomarker-positive subgroup. However, a straightforward sequential application of separately calibrated phase II designs to the two populations can inflate the probability of a false-positive efficacy conclusion. The Bayesian optimal phase II (BOP2) design uses posterior-probability thresholds for interim futility monitoring and final efficacy decisions in single-arm phase II trials. We develop a pathwise globally calibrated BOP2 framework for branching adaptive enrichment trials. At prespecified all-comer interim analyses, the trial either continues enrollment in the all-comer population or, after the all-comer futility boundary is crossed, transitions to a prespecified biomarker-positive enrichment path. The all-comer and biomarker-positive thresholds are jointly calibrated against the union of the two possible efficacy claims while accounting for the random biomarker-positive sample size available when enrichment is initiated. All decision rules remain prespecified before trial initiation. For a binary endpoint, we derive an exact finite-state recursive enumeration of the complete adaptive procedure, enabling both calibration and operating-characteristic evaluation without Monte Carlo error. Using this exact procedure, we showed that the proposed design controlled the global type I error rate under the prespecified point global null across the prespecified range of biomarker prevalence, whereas the separately calibrated BOP2 approach did not. Under alternative scenarios, efficacy claims arose through both the all-comer and biomarker-positive paths, with their relative contributions depending on biomarker prevalence and subgroup response probabilities.