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

AbstractRandomization procedures that enforce balance in prognostic factors, most commonly stratified randomization, are often employed in clinical trials. When the number of factors or factor levels is large, dynamic allocation procedures, such as the Pocock and Simon’s covariate-adaptive randomization (minimization) are preferred. In their ground-breaking work Ye and Shao (2020) identified two classes of covariate-adaptive randomization procedures. They have demonstrated theoretically that for these classes, when the model is misspecified, the robust score test (Lin and Wei, 1989) as well as the unstratified log-rank test used for analysis of time-to-event endpoints, are valid or conservative (Ye and Shao, 2020). This fact, however, was not established for minimization other than through simulations of survival endpoints. In this paper, we point out that the results of Ye and Shao can be expanded to a more general class of randomization procedures. We show, in part theoretically, in part through simulations of the within-strata imbalances, that minimization belongs to this class. Along the way we describe the asymptotic correlation matrix of the normalized within-stratum imbalances following minimization with equal prevalence of all strata. We expand the robust tests proposed by Ye and Shao for stratified randomization to minimization and examine their performance through simulations.Keywords: minimizationType I errorrobust survival analysis testsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgementsThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors would like to thank the anonymous reviewers whose recommendations substantially improved the paper.FundingThe author(s) reported there is no funding associated with the work featured in this article.