Bayesian methods for setting sample sizes and choosing allocation ratios in phase II clinical trials with time-to-event endpoints.

Conventional phase II trials using binary endpoints as early indicators of a time-to-event outcome are not always feasible. Uveal melanoma has no reliable intermediate marker of efficacy. In pancreatic cancer and viral clearance, the time to the event of interest is short, making an early indicator unnecessary. In the latter application, Weibull models have been used to analyse corresponding time-to-event data. Bayesian sample size calculations are presented for single-arm and randomised phase II trials assuming proportional hazards models for time-to-event endpoints. Special consideration is given to the case where survival times follow the Weibull distribution. The proposed methods are demonstrated through an illustrative trial based on uveal melanoma patient data. A procedure for prior specification based on knowledge or predictions of survival patterns is described. This enables investigation into the choice of allocation ratio in the randomised setting to assess whether a control arm is indeed required. The Bayesian framework enables sample sizes consistent with those used in practice to be obtained. When a confirmatory phase III trial will follow if suitable evidence of efficacy is identified, Bayesian approaches are less controversial than for definitive trials. In the randomised setting, a compromise for obtaining feasible sample sizes is a loss in certainty in the specified hypotheses: the Bayesian counterpart of power. However, this approach may still be preferable to running a single-arm trial where no data is collected on the control treatment. This dilemma is present in most phase II trials, where resources are not sufficient to conduct a definitive trial.