Pocock and Simon's minimization method is a popular approach for covariate-adaptive randomization in clinical trials. Valid statistical inference with data collected under the minimization method requires the knowledge of the limiting covariance matrix of within-stratum imbalances, whose existence is only recently established. In this work, we propose a bootstrap-based estimator for this limit and establish its consistency, in particular, by Le Cam's third lemma. As an application, we consider in simulation studies adjustments to existing robust tests for treatment effects with survival data by the proposed estimator. It shows that the adjusted tests achieve a size close to the nominal level, and unlike other designs, the robust tests without adjustment may have an asymptotic size inflation issue under the minimization method.

翻译：Pocock和Simon的最小化法是临床试验中协变量自适应随机化的一种常用方法。基于最小化法收集的数据进行有效统计推断，需要知道分层内不平衡的极限协方差矩阵，而该极限的存在性近期才被证明。本研究提出一种基于自助法的该极限估计量，并借助Le Cam第三引理证明了其一致性。作为应用，我们在模拟研究中利用所提议的估计量对现有基于生存数据的处理效应稳健检验进行了调整。结果表明，调整后的检验实际显著性水平接近名义水平，而与其他设计不同，未调整的稳健检验在最小化法下可能存在渐进显著性水平膨胀问题。