A general theory of regression adjustment for covariate-adaptive randomization: OLS, Lasso, and beyond

TL;DR

This paper develops a comprehensive theory for regression adjustment in covariate-adaptive randomized experiments, accommodating model misspecification and high-dimensional covariates, and demonstrates improved efficiency and valid inference methods.

Contribution

It unifies and extends existing results by providing a general framework for regression adjustment, including Lasso and nonparametric methods, with robust variance estimation for valid inference.

Findings

Proposes a unified theory for regression adjustment under covariate-adaptive randomization.

Demonstrates the optimality of Lasso-adjusted estimators in high-dimensional settings.

Provides nonparametric variance estimators that ensure valid inference regardless of randomization method.

Abstract

We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance the treatment allocations with respect to a few variables that are most relevant to the outcomes. Then, regression is performed in the analysis stage to adjust the remaining imbalances to yield more efficient treatment effect estimators. Building upon and unifying the recent results obtained for ordinary least squares adjusted estimators under covariate-adaptive randomization, this paper presents a general theory of regression adjustment that allows for arbitrary model misspecification and the presence of a large number of baseline covariates. We exemplify the theory on two Lasso-adjusted treatment effect estimators, both of which are optimal in their respective classes. In addition, nonparametric consistent variance estimators are proposed to facilitate valid inferences, which work irrespective of the specific randomization methods used. The robustness and improved efficiency of the proposed estimators are demonstrated through a simulation study and a clinical trial example. This study sheds light on improving treatment effect estimation efficiency by implementing machine learning methods in covariate-adaptive randomized experiments.