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.

翻译：本文研究在受试者依从性不完美的协变量自适应随机化（CARs）中，如何利用协变量回归调整提升估计效率。我们提出的回归调整估计量基于局部平均处理效应的双稳健矩，即使在分配概率异质且回归调整设定错误的情况下，仍具有一致性和渐近正态性。我们提出一种最优但可能设定错误的线性调整方法，并进一步通过非线性调整加以改进，二者均比无调整估计量具有更高效率。同时，我们给出了在CARs框架下，非参数调整与正则化调整达到半参数效率界所需的条件。