Two-Stage Double-Arm Trial Optimal Design of Restricted Mean Survival Time With Sculpted Critical Region

We propose an optimal phase II design for double-arm two-stage clinical trials using the restricted mean survival time (RMST) to measure the between-arm difference. In the superiority test of the proposed design, the null hypothesis is rejected when the between-arm RMST difference ${\hat{R}}_E-{\hat{R}}_C>m$ , and the RMST in the experimental arm ${\hat{R}}_E>q$ , where the critical values $m$ and $q$ are determined by an adaptive probability cutoff function with accumulated sample size at each stage and the asymptotic normality of RMST values. Compared to rejection rule based on ${\hat{R}}_E-{\hat{R}}_C>m$ only, the sculpted critical region requires smaller sample size based on the same type I error and power level. In the two-stage Minimax and Optimal design, simulations demonstrate that the Sculpted RMST approach offers lower total sample size, earlier interim time (smaller interim sample size under constant accrual rate), and smaller expected sample sizes compared to the log-rank test and simple RMST difference test. Besides, the method can be easily extended to multi-stage sequential design based on the adaptive probability cutoff function. The global robustness of type I error deviation when the survival parameter drift from the assumption is discussed. Implementation of the proposed design on real world trial data is also provided. The R package ScuRMST for implementing the design is now available on Github.