Statistical Inference for Covariate-Adaptive Randomization Procedures

Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming balanced treatment groups, the validity of classical statistical methods after such randomization is often unclear. In this article, we derive the theoretical properties of statistical methods based on general CAR under the linear model framework. More importantly, we explicitly unveil the relationship between covariate-adaptive and inference properties by deriving the asymptotic representations of the corresponding estimators. We apply the proposed general theory to various randomization procedures such as complete randomization, rerandomization, pairwise sequential randomization, and Atkinson’s DA-biased coin design and compare their performance analytically. Based on the theoretical results, we then propose a new approach to obtain valid and more powerful tests. These results open a door to understand and analyze experiments based on CAR. Simulation studies provide further evidence of the advantages of the proposed framework and the theoretical results. Supplementary materials for this article are available online.协变量自适应随机化（Covariate-adaptive randomization, CAR）方法在对照研究中被广泛应用，旨在提升不同处理组间的协变量平衡水平。然而，由于此类随机化方法在构建均衡处理组时不可避免地会用到协变量信息，经该类随机化后的经典统计方法的有效性往往尚不明确。本文在线性模型框架下，推导了基于一般协变量自适应随机化方法的统计工具的理论性质。更为重要的是，本文通过推导对应估计量的渐近表达式，明确揭示了协变量自适应随机化与统计推断性质之间的内在关联。我们将所提出的一般理论应用于多种随机化程序，包括完全随机化、再随机化、配对序贯随机化以及阿特金森DA偏硬币设计，并通过解析方法对比其性能表现。基于上述理论结果，本文进一步提出了一种能够构建有效且功效更优检验的新方法。此类研究成果为理解与分析基于协变量自适应随机化的实验提供了全新视角。模拟研究进一步证实了本文所提框架与理论结果的优越性。本文的补充材料可在线获取。