The impact of misclassification on covariate-adaptive randomized clinical trials with generalized linear models

Covariate-adaptive randomization (CAR) is a type of randomization method that uses covariate information to enhance the comparability between different treatment groups. Under such randomization, the covariate is usually well balanced, i.e., the imbalance between the treatment group and placebo group is controlled. In practice, the covariate is sometimes misclassified. The covariate misclassification affects the CAR itself and statistical inferences after the CAR. In this paper, we examine the impact of covariate misclassification on CAR from two aspects. First, we study the balancing properties of CAR with unequal allocation in the presence of covariate misclassification. We show the convergence rate of the imbalance and compare it with that under true covariate. Second, we study the hypothesis test under CAR with misclassified covariates in a generalized linear model (GLM) framework. We consider both the unadjusted and adjusted models. To illustrate the theoretical results, we discuss the validity of test procedures for three commonly-used GLM, i.e., logistic regression, Poisson regression and exponential model. Specifically, we show that the adjusted model is often invalid when the misclassified covariates are adjusted. In this case, we provide a simple correction for the inflated Type-I error. The correction is useful and easy to implement because it does not require misclassification specification and estimation of the misclassification rate. Our study enriches the literature on the impact of covariate misclassification on CAR and provides a practical approach for handling misclassification.