Validity of tests for time-to-event endpoints in studies with the Pocock and Simon covariate-adaptive randomization

TL;DR

This paper investigates the validity of tests for time-to-event endpoints under covariate-adaptive randomization, extending previous results to Pocock and Simon procedures and analyzing their correlation structures and test performances.

Contribution

It generalizes theoretical results on test validity to Pocock and Simon covariate-adaptive randomization and explores their correlation structures and test performance through simulations.

Findings

Pocock and Simon randomization belongs to the class where tests are conservative when models are misspecified.

The asymptotic correlation matrix for within-stratum imbalances is derived for equal stratum prevalence.

Robust tests are extended and evaluated for minimization procedures, showing their performance.

Abstract

In the presence of prognostic covariates, inference about the treatment effect with time-to-event endpoints is mostly conducted via the stratified log-rank test or the score test based on the Cox proportional hazards model. In their ground-breaking work Ye and Shao (2020) have demonstrated theoretically that when the model is misspecified, the robust score test (Wei and Lin, 1989) as well as the unstratified log-rank test are conservative in trials with stratified randomization. This fact, however, was not established for the Pocock and Simon covariate-adaptive allocation other than through simulations. In this paper, we expand the results of Ye and Shao to a more general class of randomization procedures and show, in part theoretically, in part through simulations, that the Pocock and Simon covariate-adaptive allocation belongs to this class. We also advance the search for the correlation structure of the normalized within-stratum imbalances with minimization by describing the asymptotic correlation matrix for the case of equal prevalence of all strata. We expand the robust tests proposed by Ye and Shao for stratified randomization to minimization and examine their performance trough simulations.