Statistical Inference of Covariate-Adjusted Randomized Experiments
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Covariate-adjusted randomization procedure is frequently used in comparative studies to increase the covariate balance across treatment groups. However, as the randomization inevitably uses the covariate information when forming balanced treatment groups, the validity of classical statistical methods following such randomization is often unclear. In this article, we derive the theoretical properties of statistical methods based on general covariate-adjusted randomization under the linear model framework. More importantly, we explicitly unveil the relationship between covariate-adjusted 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 (CR), rerandomization (RR), pairwise sequential randomization (PSR), and Atkinson's D_A-biased coin design (D_A-BCD), 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 covariate-adjusted randomization. Simulation studies provide further evidence of the advantages of the proposed framework and theoretical results.
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