Bayesian phase II adaptive randomization by jointly modeling efficacy and toxicity as time-to-event outcomes.

The main goals of Phase II trials are to identify the therapeutic efficacy of new treatments and continue monitoring all the possible adverse effects. In Phase II trials, it is important to develop an adaptive randomization (AR) procedure that takes into account both the efficacy and toxicity. In most existing articles, toxicity is modeled as a binary endpoint through an unobservable random effect (frailty) to link the efficacy and toxicity. However, this approach does not capture toxicity profiles that evolve over time. In this article, we propose a new Bayesian adaptive randomization (BAR) procedure using the covariate-adjusted efficacy-toxicity ratio (ETR) index, where efficacy and toxicity are jointly modelled as time-to-event (TTE) outcomes. Furthermore, we also propose early stopping rules for toxicity and futility such that inferior treatments can be dropped at earlier time of trial. Simulation results show that compared to the BAR procedures based solely on the efficacy and that based on TTE efficacy and binary toxicity outcomes, the proposed BAR procedure can better identify the difference in treatment toxicity such that it can assign more patients to the superior treatment arm under some scenarios.