协变量数量发散的协变量自适应随机化的理论性质
Theoretical Properties of Covariate-Adaptive Randomization with a Diverging Number of Covariates
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中文总结 AI 辅助
本文研究高维设定下两类协变量自适应随机化程序的理论性质，建立指定协变量不均衡性的收敛速率，推导均值差估计量的渐近性质并构建95%置信区间，通过数值与实证研究验证结果的实际价值。
中文摘要 AI 辅助
协变量自适应随机化程序被广泛应用于临床试验中，以改善协变量均衡性。在现代应用中，实验者通常可获取大量协变量，这催生了对协变量数量发散的协变量自适应随机化程序理论的需求。本文在高维设定下研究两类统一协变量自适应随机化程序的理论性质，对这两类程序，我们建立了对应指定协变量的不均衡性测度的收敛速率。此外，对其中一类程序，我们研究了未指定协变量的不均衡性的渐近性质，并将这些结果应用于推导平均处理效应的均值差估计量的渐近性质，构建渐近95%置信区间。进一步，我们提供了大量数值和实证研究，以说明理论结果的实际相关性。
英文摘要
Covariate-adaptive randomization procedures are widely used in clinical trials to improve covariate balance. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate-adaptive randomization procedures with a diverging number of covariates. This paper studies two classes of covariate-adaptive randomization procedures, referred to as imbalance-efficient covariate-adaptive randomization and imbalance-robust covariate-adaptive randomization, when the feature dimension diverges. We derive convergence rates for the imbalance of the covariates used in randomization. For both procedures, the imbalance is of a smaller order than that under complete randomization when the feature dimension is $o(n)$, whereas it is of the same order when the feature dimension is $Ω(n)$. For imbalance-robust covariate-adaptive randomization, we further establish the asymptotic properties of the imbalance of additional covariates and use these results to derive the asymptotic distribution of the difference-in-means estimator for the average treatment effect and construct asymptotically valid confidence intervals. Furthermore, we provide extensive numerical and empirical studies to illustrate the practical relevance of our theoretical results.
