Bayesian enhancement two-stage design with error control for phase II clinical trials

Phase II clinical trials make a critical decision of go or no-go to a subsequent phase III studies. A considerable proportion of promising drugs identified in phase II trials fail the confirmative efficacy test in phase III. Recognizing the low posterior probabilities of H₁ when accepting the drug under Simon's two-stage design, the Bayesian enhancement two-stage (BET) design is proposed to strengthen the passing criterion. Under the BET design, the lengths of highest posterior density (HPD) intervals, posterior probabilities of H₀ and H₁ are computed to calibrate the design parameters, aiming to improve the stability of the trial characteristics and strengthen the evidence for proceeding the drug development forward. However, from a practical perspective, the HPD interval length lacks transparency and interpretability. To circumvent this problem, we propose the BET design with error control (BETEC) by replacing the HPD interval length with the posterior error rate. The BETEC design can achieve a balance between the posterior false positive rate and false negative rate and, more importantly, it has an intuitive and clear interpretation. We compare our method with the BET design and Simon's design through extensive simulation studies. As an illustration, we further apply BETEC to two recent clinical trials, and investigate its performance in comparison with other competitive designs. Being both efficient and intuitive, the BETEC design can serve as an alternative toolbox for implementing phase II single-arm trials.