Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance

TL;DR

This paper develops regression-adjusted estimators for covariate-adaptive randomizations with imperfect compliance, enhancing efficiency and robustness even under misspecification and heterogeneity.

Contribution

It introduces doubly robust regression adjustments, including linear and nonlinear methods, that improve estimation efficiency in covariate-adaptive randomizations with imperfect compliance.

Findings

Regression-adjusted estimators are consistent and asymptotically normal.

Optimal linear and nonlinear adjustments improve efficiency over unadjusted methods.

Conditions are provided for nonparametric and regularized adjustments to reach semiparametric efficiency.

Abstract

We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust moment for local average treatment effects, are consistent and asymptotically normal even with heterogeneous probability of assignment and misspecified regression adjustments. We propose an optimal but potentially misspecified linear adjustment and its further improvement via a nonlinear adjustment, both of which lead to more efficient estimators than the one without adjustments. We also provide conditions for nonparametric and regularized adjustments to achieve the semiparametric efficiency bound under CARs.