A General Form of Covariate Adjustment in Randomized Clinical Trials

In randomized clinical trials, adjusting for baseline covariates has been advocated as a way to improve credibility and efficiency for demonstrating and quantifying treatment effects. This article studies the augmented inverse propensity weighted (AIPW) estimator, which is a general form of covariate adjustment that includes approaches using linear and generalized linear models and machine learning models. Under covariate-adaptive randomization, we establish a general theorem that shows a complete picture about the asymptotic normality, efficiency gain, and applicability of AIPW estimators. Based on the general theorem, we provide insights on the conditions for guaranteed efficiency gain and universal applicability under different randomization schemes, which also motivate a joint calibration strategy using some constructed covariates after applying AIPW. We illustrate the application of the general theorem with two examples, the generalized linear model and the machine learning model. We provide the first theoretical justification of using machine learning methods with dependent data under covariate-adaptive randomization. Our methods are implemented in the R package RobinCar.