Balancing Unobserved Covariates With Covariate-Adaptive Randomized Experiments

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.

在临床试验与因果推断领域，平衡关键协变量往往至关重要。分层区组随机化（Stratified Permuted Block, STR-PB）与协变量自适应随机化（Covariate-Adaptive Randomization, CAR）两类方法在实际场景中被广泛用于平衡已观测协变量。上述方法针对已观测协变量的平衡特性已得到充分研究，但学界仍存在疑问：这类方法能否在未观测协变量层面同样实现良好的平衡效果。本文构建了一套用于分析未观测协变量失衡问题的通用分析框架，所得结果可用于推导并比较完全随机化（Complete Randomization, CR）、STR-PB及CAR三类方法针对未观测协变量的平衡特性。为量化使用STR-PB与CAR方法相较CR方法所获得的性能提升，本文引入了未观测协变量失衡的方差缩减率指标并展开比较分析。研究结果表明，当分层数相较于样本规模较小时，采用CAR或STR-PB方法在未观测协变量的平衡层面可展现出显著优势。本研究成果同时为未来探索协变量自适应随机化临床试验及其他诸多应用场景中未观测协变量的影响铺平了道路。本文的补充材料可在线获取。