Marginal design, also called as the minimization method, is a popular approach used for covariate adaptive randomization when the number of strata is large in a clinical trial. It aims to achieve a balanced allocation of treatment groups at the marginal levels of some prespecified and discrete stratification factors. Valid statistical inference with data collected under covariate adaptive randomization requires the knowledge of the limiting covariance matrix of within-stratum imbalances. The existence of the limit under the marginal design is recently established, which can be estimated by Monte Carlo simulations when the distribution of the stratification factors is known. This assumption may not hold, however, in practice. In this work, we propose to replace the usually unknown distribution with an estimator, such as the empirical distribution, in the Monte Carlo approach 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 covariances 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 marginal design.
翻译:边际设计,也称为最小化方法,是一种在临床试验中各层数量众多时用于共变适应随机化的流行方法,目的是在一些预先指定和离散的分层因素的边缘水平上均衡分配治疗组,对在共变适应随机化下收集的数据进行有效的统计推断,需要了解底层不平衡的有限共变矩阵;边际设计下存在极限,在已知分层因素分布时,蒙特卡洛模拟可以估计这种极限,但在实践中,这一假设可能无法维持。在这项工作中,我们提议将通常不为人所知的分布用一个估测器取代通常为未知的分布,例如蒙特卡洛方法中的经验分布,并确立其一致性,特别是勒卡姆的第三个利姆马。作为一项应用,我们考虑在模拟研究中调整现有可靠的检验结果,以拟议调控点估算师的求得的求得的存活数据来进行治疗效果测试。它表明,经调整的测试的规模接近名义水平,但与其他设计不同的是,在边际设计下,稳健的测试可能具有边缘性通货膨胀问题。