  Many phase II clinical trials have used survival outcomes as the primary
endpoints in recent decades. Suppose the radiotherapy is evaluated in a phase
II trial using survival outcomes. In that case, the competing risk issue often
arises because the time to disease progression can be censored by the time to
normal tissue complications, and vice versa. Besides, much literature has
examined that patients receiving the same radiotherapy dose may yield distinct
responses due to their heterogeneous radiation susceptibility statuses.
Therefore, the "one-dose-fit-all" strategy often fails, and it is more relevant
to evaluate the subgroup-specific treatment effect with the subgroup defined by
the radiation susceptibility status. In this paper, we propose a Bayesian
precision phase II trial design evaluating the subgroup-specific treatment
effects of radiotherapy. We use the cause-specific hazard approach to model the
competing risk survival outcomes. We propose restricting the candidate
radiation doses based on each patient's radiation susceptibility status. Only
the clinically feasible personalized dose will be considered, which enhances
the benefit for the patients in the trial. In addition, we propose a stratified
Bayesian adaptive randomization scheme such that more patients will be
randomized to the dose reporting more favorable survival outcomes. Numerical
studies have shown that the proposed design performed well and outperformed the
conventional design ignoring the competing risk issue.
