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Many phase II clinical trials have used survival outcomes as the primaryendpoints in recent decades. Suppose the radiotherapy is evaluated in a phaseII trial using survival outcomes. In that case, the competing risk issue oftenarises because the time to disease progression can be censored by the time tonormal tissue complications, and vice versa. Besides, much literature hasexamined that patients receiving the same radiotherapy dose may yield distinctresponses due to their heterogeneous radiation susceptibility statuses.Therefore, the "one-dose-fit-all" strategy often fails, and it is more relevantto evaluate the subgroup-specific treatment effect with the subgroup defined bythe radiation susceptibility status. In this paper, we propose a Bayesianprecision phase II trial design evaluating the subgroup-specific treatmenteffects of radiotherapy. We use the cause-specific hazard approach to model thecompeting risk survival outcomes. We propose restricting the candidateradiation doses based on each patient's radiation susceptibility status. Onlythe clinically feasible personalized dose will be considered, which enhancesthe benefit for the patients in the trial. In addition, we propose a stratifiedBayesian adaptive randomization scheme such that more patients will berandomized to the dose reporting more favorable survival outcomes. Numericalstudies have shown that the proposed design performed well and outperformed theconventional design ignoring the competing risk issue.

A Bayesian Precision Response-adaptive Phase II Clinical Trial Design for Radiotherapies with Competing Risk Survival Outcomes