A Bayesian Treatment Selection Design for Phase II Randomised Cancer Clinical Trials

It is crucial to design Phase II cancer clinical trials that balance the efficiency of treatment selection with clinical practicality. Sargent and Goldberg proposed a frequentist design that allows decision-making even when the primary endpoint is ambiguous. However, frequentist approaches rely on fixed thresholds and long-run frequency properties, which can limit flexibility in practical applications. In contrast, the Bayesian decision rule, based on posterior probabilities, enables transparent decision-making by incorporating prior knowledge and updating beliefs with new data, addressing some of the inherent limitations of frequentist designs. In this study, we propose a novel Bayesian design, allowing the selection of the best-performing treatment. Specifically, concerning phase II clinical trials with a binary outcome, our decision rule employs posterior interval probability by integrating the joint distribution over all values, for which the 'success rate' of the best-performing treatment is greater than that of the others. This design can then determine which treatment should proceed to the next phase, given predefined decision thresholds. Furthermore, we propose two sample size determination methods to empower such treatment selection designs implemented in a Bayesian framework. Through simulation studies and real-data applications, we demonstrate how this approach can overcome challenges related to sample size constraints in randomised trials. In addition, we present a user-friendly R Shiny application, enabling clinicians to conduct Bayesian designs. Both our methodology and the software application can advance the design and analysis of clinical trials for evaluating cancer treatments.