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Pocock and Simon's minimization method is a popular approach forcovariate-adaptive randomization in clinical trials. Valid statisticalinference with data collected under the minimization method requires theknowledge of the limiting covariance matrix of within-stratum imbalances, whoseexistence is only recently established. In this work, we propose abootstrap-based estimator for this limit and establish its consistency, inparticular, by Le Cam's third lemma. As an application, we consider insimulation studies adjustments to existing robust tests for treatment effectswith survival data by the proposed estimator. It shows that the adjusted testsachieve a size close to the nominal level, and unlike other designs, the robusttests without adjustment may have an asymptotic size inflation issue under theminimization method.

Consistent Covariance estimation for stratum imbalances under minimization method for covariate-adaptive randomization