Some design considerations incorporating early futility for single-arm clinical trials with time-to-event primary endpoints using Weibull distribution

Sample size calculation is an essential component of the planning phase of a clinical trial. In the context of single-arm clinical trials with time-to-event (TTE) endpoints, only a few options with limited design features are available. Motivated from ethical or practical considerations, two-stage designs are implemented for single-arm studies to obtain early evidence of futility. A major drawback of such designs is that early stopping may only occur at the conclusion of the first stage, even if lack of efficacy becomes apparent at any other time point over the course of the clinical trial. In this manuscript, we attempt to fill some existing gaps in the literature related to single-arm clinical trials with TTE endpoints. We propose a parametric maximum likelihood estimate-based test whose variance component accounts for the expected proportion of loss to follow-up and different accrual patterns (early, late, or uniform accrual). For the proposed method, we present three stochastic curtailment methods (conditional power, predictive power, Bayesian predictive probability) which can be employed for efficacy or futility testing purposes. Finally, we discuss the implementation of group sequential designs for obtaining an early evidence of efficacy or futility at pre-planned timings of interim analyses. Through extensive simulations, it is shown that our proposed method performs well for designing these studies with moderate to large sample sizes. Some examples are presented to demonstrate various aspects of the stochastic curtailment and repeated significance testing methods presented in this manuscript.