Blinded sample-size re-estimation for the restricted mean survival time via the worst-case variance evaluation using mathematical programming

Music City Center 

Restricted mean survival time (RMST)-based analysis is becoming more popular as an alternative to the conventional logrank-hazard ratio approach when comparing the survival benefits of two interventions in randomized clinical trials. When the logrank test is the primary analysis, an event-driven design is used to achieve the target power to detect a specified treatment effect measured by the hazard ratio. However, this approach is not applicable when employing the RMST-based test because the power does not depend solely on the number of observed events and the between-group difference measured by RMST but by parameters such as event and censoring time distributions. If these parameters are not correctly specified in calculating the required sample size in the design stage, the study may not have the targeted power to detect a specified difference in RMST. To avoid this, we propose a blind sample size re-estimation method for the RMST-based test. We consider the survival function estimated with the pooled sample in a blind review as constraints for the survival functions of the two groups. Under the constraints, the maximum variance for the RMST difference and the corresponding sample size are calculated using non-linear programming. The resulting sample size will represent the worst-case scenario, or the upper bound of the required sample size needed to achieve the target power to detect the specified RMST difference. Our comprehensive numerical studies indicated that the proposed method effectively circumvents the potential underestimation of the required sample size due to the misspecification of survival functions in the design stage.

Blinded sample size re-estimation

Nonproportional hazards

Non-linear programing

Restricted mean survival time