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We investigate how to improve efficiency using regression adjustments withcovariates in covariate-adaptive randomizations (CARs) with imperfect subjectcompliance. Our regression-adjusted estimators, which are based on the doublyrobust moment for local average treatment effects, are consistent andasymptotically normal even with heterogeneous probability of assignment andmisspecified regression adjustments. We propose an optimal but potentiallymisspecified linear adjustment and its further improvement via a nonlinearadjustment, both of which lead to more efficient estimators than the onewithout adjustments. We also provide conditions for nonparametric andregularized adjustments to achieve the semiparametric efficiency bound underCARs.

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