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