论文标题
关于协变量自适应设计的理论
On the Theory of Covariate-Adaptive Designs
论文作者
论文摘要
Pocock和Simon的边际程序（Pocock and Simon，1975）通常在临床试验中实施了对影响力协变量的强制性治疗分配。但是，数十年来，Pocock和Simion程序的理论特性在很大程度上一直难以捉摸。在本文中，我们为协变量自适应设计提出了一个一般框架，并在广泛满足的条件下建立了相应的理论。作为一种特殊情况，我们获得了Pocock和Simon的边际程序的理论特性：边际失衡和总体失衡的概率有限，但随着$ \ sqrt {n} $的速率随着样本尺寸的增加而增加，层内不平衡的增加。理论结果提供了有关协变量自适应随机化程序的平衡特性的新见解，并为基于协变量自适应随机过程的临床试验的统计学推断打开了一扇门。
Pocock and Simon's marginal procedure (Pocock and Simon, 1975) is often implemented forbalancing treatment allocation over influential covariates in clinical trials. However, the theoretical properties of Pocock and Simion's procedure have remained largely elusive for decades. In this paper, we propose a general framework for covariate-adaptive designs and establish the corresponding theory under widely satisfied conditions. As a special case, we obtain the theoretical properties of Pocock and Simon's marginal procedure: the marginal imbalances and overall imbalance are bounded in probability, but the within-stratum imbalances increase with the rate of $\sqrt{n}$ as the sample size increases. The theoretical results provide new insights about balance properties of covariate-adaptive randomization procedures and open a door to study the theoretical properties of statistical inference for clinical trials based on covariate-adaptive randomization procedures.
