Asymptotic Properties of Multi-Treatment Covariate Adaptive Randomization Procedures for Balancing Observed and Unobserved Covariates
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平衡已观测与未观测协变量的多处理协变量自适应随机化：渐近性质
- 研究问题
- 多处理临床试验中，协变量自适应随机化能否同时平衡离散、连续及交互特征，并在分析遗漏协变量时支持可靠效应检验？
- 方法与思路
- 作者建立涵盖多类协变量特征的随机化框架，分析观测与未观测协变量的不平衡收敛率，并研究异方差线性模型下的检验。
- 材料陈述的贡献
- 摘要称，观测特征不平衡可达 O_P(1)，未观测协变量为 O_P(√n)，并提出工作模型错误时仍有渐近正确一类错误率的检验。
- 阅读关注点
- 应核对随机化程序与收敛率条件、未观测协变量的限制，以及模型误设下检验有效性的范围和方差估计方式。
- 阅读边界
- 依据 arXiv 预印本摘要，同行评审或接收未核实；具体条件和检验构造未说明，不能把未观测不平衡率理解为已消除混杂。
原文摘要
Applications of CAR for balancing continuous covariates remain comparatively rare, especially in multi-treatment clinical trials, and the theoretical properties of multi-treatment CAR have remained largely elusive for decades. In this paper, we consider a general framework of CAR procedures for multi-treatment clinal trials which can balance general covariate features, such as quadratic and interaction terms which can be discrete, continuous, and mixing. We show that under widely satisfied conditions the proposed procedures have superior balancing properties; in particular, the convergence rate of imbalance vectors can attain the best rate $O_P(1)$ for discrete covariates, continuous covariates, or combinations of both discrete and continuous covariates, and at the same time, the convergence rate of the imbalance of unobserved covariates is $O_P(\sqrt n)$, where $n$ is the sample size. The general framework unifies many existing methods and related theories, introduces a much broader class of new and useful CAR procedures, and provides new insights and a complete picture of the properties of CAR procedures. The favorable balancing properties lead to the precision of the treatment effect test in the presence of a heteroscedastic linear model with dependent covariate features. As an application, the properties of the test of treatment effect with unobserved covariates are studied under the CAR procedures, and consistent tests are proposed so that the test has an asymptotic precise type I error even if the working model is wrong and covariates are unobserved in the analysis.