Abstract

Balancing important covariates is often critical in clinical trials and causal inference. Stratified permuted block (STR-PB) and covariate-adaptive randomization (CAR) procedures are widely used to balance observed covariates in practice. The balance properties of these procedures with respect to the observed covariates have been well studied. However, it has been questioned whether these methods will also yield a good balance for the unobserved covariates. In this article, we develop a general framework for the analysis of the unobserved covariates imbalance. These results are applicable to develop and compare the balance properties of complete randomization (CR), STR-PB, and CAR procedures with respect to the unobserved covariates. To quantify the improvement obtained by using STR-PB and CAR procedures rather than CR, we introduce the percentage reduction in variance of the unobserved covariates imbalance and compare these quantities. Our results demonstrate the benefits of using CAR or STR-PB (when the number of strata is small relative to the sample size) in terms of balancing unobserved covariates. These results also pave the way for future research into the effect of unobserved covariates in covariate-adaptive randomized experiments in clinical trials, as well as many other applications. Supplementary materials for this article are available online.

摘要

平衡重要的协变量在临床试验和因果推断中通常至关重要。分层置换块 (STR-PB) 和协变量自适应随机化 (CAR) 程序在实践中被广泛用于平衡观察到的协变量。这些程序相对于观察到的协变量的平衡特性已经得到了很好的研究。然而，人们质疑这些方法是否也会为未观察到的协变量产生良好的平衡。在本文中，我们开发了一个分析未观察到的协变量不平衡的通用框架。这些结果适用于开发和比较完全随机化 (CR)、STR-PB 和 CAR 程序相对于未观察到的协变量的平衡特性。为了量化使用 STR-PB 和 CAR 程序而不是 CR 获得的改进，我们引入了未观察到的协变量不平衡的方差百分比减少并比较了这些数量。我们的结果证明了使用 CAR 或 STR-PB（当层数相对于样本量较小时）在平衡未观察到的协变量方面的好处。这些结果也为未来研究未观察到的协变量在临床试验中协变量自适应随机实验以及许多其他应用中的影响铺平了道路。本文的补充材料可在线获取。这些结果也为未来研究未观察到的协变量在临床试验中协变量自适应随机实验以及许多其他应用中的影响铺平了道路。本文的补充材料可在线获取。这些结果也为未来研究未观察到的协变量在临床试验中协变量自适应随机实验以及许多其他应用中的影响铺平了道路。本文的补充材料可在线获取。