A New and Unified Family of Covariate Adaptive Randomization Procedures and Their Properties

In clinical trials and other comparative studies, covariate balance is crucial for credible and efficient assessment of treatment effects. Covariate adaptive randomization (CAR) procedures are extensively used to reduce the likelihood of covariate imbalances occurring. In the literature, most studies have focused on balancing of discrete covariates. Applications of CAR with continuous covariates remain rare, especially when the interest goes beyond balancing only the first moment. In this article, we propose a family of CAR procedures that can balance general covariate features, such as quadratic and interaction terms. Our framework not only unifies many existing methods, but also introduces a much broader class of new and useful CAR procedures. We show that the proposed procedures have superior balancing properties; in particular, the convergence rate of imbalance vectors is OP(nϵ) for any ϵ>0 if all of the moments are finite for the covariate features, relative to OP(n) under complete randomization, where n is the sample size. Both the resulting convergence rate and its proof are novel. These favorable balancing properties lead to increased precision of treatment effect estimation in the presence of nonlinear covariate effects. The framework is applied to balance covariate means and covariance matrices simultaneously. Simulation and empirical studies demonstrate the excellent and robust performance of the proposed procedures. Supplementary materials for this article are available online.