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In the presence of prognostic covariates, inference about the treatmenteffect with time-to-event endpoints is mostly conducted via the stratifiedlog-rank test or the score test based on the Cox proportional hazards model. Intheir ground-breaking work Ye and Shao (2020) have demonstrated theoreticallythat 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 withstratified randomization. This fact, however, was not established for thePocock 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 ofrandomization procedures and show, in part theoretically, in part throughsimulations, that the Pocock and Simon covariate-adaptive allocation belongs tothis class. We also advance the search for the correlation structure of thenormalized within-stratum imbalances with minimization by describing theasymptotic correlation matrix for the case of equal prevalence of all strata.We expand the robust tests proposed by Ye and Shao for stratified randomizationto minimization and examine their performance trough simulations.

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