Theoretical Properties of Covariate-Adaptive Randomization with a Diverging Number of Covariates

Covariate-adaptive randomization procedures are widely used in clinical trials to improve covariate balance. In modern applications, experimenters often have access to many covariates, motivating the need for a theory of covariate-adaptive randomization procedures with a diverging number of covariates. In this paper, we study the theoretical properties of two unified families of covariate-adaptive randomization procedures under high-dimensional settings. For the two procedures, we establish the convergence rate of the imbalance measure corresponding to the specified covariates. In addition, for one of them, we study the asymptotic properties of the imbalance of unspecified covariates under and apply these results to derive the asymptotic properties of the difference-in-means estimator for the average treatment effect and construct asymptotic 95% confidence intervals. Furthermore, we provide extensive numerical and empirical studies to illustrate the practical relevance of our theoretical results.