Randomization-based covariance analysis for hypothesis testing of treatment comparisons based on restricted mean survival time with categorized time-to-event data.

Abstract

This paper introduces randomization-based analysis of covariance (RB-ANCOVA) for hypothesis testing of restricted mean survival time (RMST) differences between two randomized treatments in trials with categorized time-to-event data. RMST treatment differences over a prespecified time period are clinically meaningful and avoid assumptions like proportional hazards. The proposed method tests the strong null hypothesis that each participant's time-to-event would remain unchanged regardless of treatment assignment. Covariate adjustment is achieved by constraining baseline covariate means to be equal across arms, which reduces variance. The follow-up period is partitioned into mutually exclusive intervals, and RMST is approximated as the area under the survival curve. Under the strong null hypothesis, the joint asymptotic covariance structure of RMST and covariate means is known and used to construct a chi-squared test statistic for the covariate-adjusted RMST difference. The method accommodates stratified trial designs and supports hypothesis testing over single or several time intervals, enabling testing within internal intervals. The difference in RMSTs over an interval can be divided by its length to yield an average survival rate difference. Additionally, the approach allows the computation of essentially exact p-values via re-randomization. We illustrate the method with data from a randomized, placebo-controlled trial evaluating a test treatment for amyotrophic lateral sclerosis. This method provides a hypothesis testing approach for RMST treatment differences that leverages RB-ANCOVA to adjust for their correlations with baseline covariate differences. Under the strong null hypothesis, it enables hypothesis testing with clear control of Type I error and reduced variance without relying on model-based assumptions.