  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.
