Statistical Inference for Covariate-Adaptive Randomization Procedures With Missing Covariates

Covariate-adaptive randomization (CAR) is increasingly used in clinical trials to balance baseline covariates, and its statistical properties have therefore attracted considerable attention in recent years. However, most existing studies overlook the issue of missing covariates, which is a common occurrence in practice. In this paper, we establish the theoretical properties of hypothesis testing for treatment and covariate effects when missing covariates are imputed using the single imputation method. The results indicate that the traditional test is conservative under certain conditions. However, this conservativeness can be corrected using an adjusted test, leading to higher statistical power. Furthermore, we extend our framework to the multiple imputation setting and compare its performance with single imputation through simulations. Our results provide a theoretical foundation for applying CAR procedures in the presence of missing covariates.