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.

中文翻译：

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协变量自适应随机化最小化方法下层不平衡的一致协方差估计

Pocock 和 Simon 的最小化方法是临床试验中协变量自适应随机化的流行方法。利用最小化方法收集的数据进行有效的统计推断需要了解层内不平衡的极限协方差矩阵，而该矩阵的存在最近才被确定。在这项工作中，我们针对这个极限提出了一个基于引导的估计器，并建立了它的一致性，特别是通过勒卡姆的第三个引理。作为一种应用，我们在模拟研究中考虑对现有稳健的治疗效果测试进行调整，并使用所提出的估计器的生存数据。结果表明，调整后的测试达到了接近名义水平的规模，并且与其他设计不同，未经调整的稳健测试在最小化方法下可能会出现渐近规模膨胀问题。