Power and Sample Size Calculations for the Restricted Mean Time Analysis of Prioritized Composite Endpoints

Abstract

As a new way of reporting treatment effect, the restricted mean time in favor (RMT-IF) of treatment measures the net average time the treated have had a less serious outcome than the untreated over a specified time window. With multiple outcomes of differing severity, this offers a more interpretable and data-efficient alternative to the prototypical restricted mean (event-free) survival time. To facilitate its adoption in actual trials, we develop simple approaches to power and sample size calculations and implement them in user-friendly R programs. In doing so we model the bivariate outcomes of death and a nonfatal event using a Gumbel–Hougaard copula with component-wise proportional hazards structures, under which the RMT-IF estimand is derived in closed form. In a standard set-up for censoring, the variance of the nonparametric effect-size estimator is simplified and computed via a hybrid of numerical and Monte Carlo integrations, allowing us to compute the power and sample size as functions of component-wise hazard ratios. Simulation studies show that these formulas provide accurate approximations in realistic settings. To illustrate our methods, we consider designing a new trial to evaluate treatment effect on the composite outcomes of death and cancer relapse in lymph node-positive breast cancer patients, with baseline parameters calculated from a previous study.