An Optimal Method for Covariate Balancing and Its Properties

This article introduces a new randomization procedure to improve the covariate balance across treatment groups. Covariate balance is one of the most important concerns for successful comparative studies, such as causal inference and clinical trials, because it reduces bias and improves the accuracy of inference. However, chance imbalance may still exist in traditional randomized experiments, in which units are randomly allocated without using their covariate information. To address this issue, the proposed method allocates the units sequentially and adaptively, using information on the current level of imbalance and the incoming unit's covariate. With a large number of covariates or a large number of units, the proposed method shows substantial advantages over the traditional methods in terms of the covariate balance and computational time, making it an ideal technique in the era of big data. Furthermore, the proposed method attains the optimal covariate balance, in the sense that the estimated average treatment effect under the proposed method attains its minimum variance asymptotically. Numerical studies and real data analysis provide further evidence of the advantages of the proposed method.