The impact of misclassification on covariate-adaptive randomized clinical trials

Covariate-adaptive randomization (CAR) is widely used in clinical trials to balance treatment allocation over covariates. Over the past decade, significant progress has been made on the theoretical properties of covariate-adaptive design and associated inference. However, most results are established under the assumption that the covariates are correctly measured. In practice, measurement error is inevitable, resulting in misclassification for discrete covariates. When covariate misclassification is present in a clinical trial conducted using CAR, the impact is twofold: it impairs the intended covariate balance, and raises concerns over the validity of test procedures. In this paper, we consider the impact of misclassification on covariate-adaptive randomized trials from the perspectives of both design and inference. We derive the asymptotic normality, and thereby the convergence rate, of the imbalance of the true covariates for a general family of covariate-adaptive randomization methods, and show that a superior covariate balance can still be attained compared to complete randomization. We also show that the two sample t-test is conservative, with a reduced Type I error, but that this can be corrected using a bootstrap method. Moreover, if the misclassified covariates are adjusted in the model used for analysis, the test maintains its nominal Type I error, with an increased power. Our results support the use of covariate-adaptive randomization in clinical trials, even when the covariates are subject to misclassification.