Sample Size Reestimation in Stochastic Curtailment Tests With Time‐to‐Events Outcome in the Case of Nonproportional Hazards Utilizing Two Weibull Distributions With Unknown Shape Parameters

ABSTRACT

Stochastic curtailment tests for Phase II two‐arm trials with time‐to‐event end points are traditionally performed using the log‐rank test. Recent advances in designing time‐to‐event trials have utilized the Weibull distribution with a known shape parameter estimated from historical studies. As sample size calculations depend on the value of this shape parameter, these methods either cannot be used or likely underperform/overperform when the natural variation around the point estimate is ignored. We demonstrate that when the magnitude of the Weibull shape parameters changes, unblinded interim information on the shape of the survival curves can be useful to enrich the final analysis for reestimation of the sample size. For such scenarios, we propose two Bayesian solutions to estimate the natural variations of the Weibull shape parameter. We implement these approaches under the framework of the newly proposed relative time method that allows nonproportional hazards and nonproportional time. We also demonstrate the sample size reestimation for the relative time method using three different approaches (internal pilot study approach, conditional power, and predictive power approach) at the interim stage of the trial. We demonstrate our methods using a hypothetical example and provide insights regarding the practical constraints for the proposed methods.