Adaptive Randomization via Mahalanobis Distance

In comparative studies, researchers often seek an optimal covariate balance. However, chance imbalance still exists in randomized experiments, and becomes more serious as the number of covariates increases. To address this issue, we introduce a new randomization procedure, called adaptive randomization via the Mahalanobis distance (ARM). The proposed method allocates units sequentially and adaptively, using information on the current level of imbalance and the incoming unit’s covariate. Theoretical results and numerical comparison show that with a large number of covariates or a large number of units, the proposed method shows substantial advantages over traditional methods in terms of the covariate balance, estimation accuracy, hypothesis testing power, and computational time. The proposed method attains the optimal covariate balance, in the sense that the estimated treatment effect attains its minimum variance asymptotically, and can be applied in both causal inference and clinical trials. Lastly, numerical stud1 Statistica Sinica: Preprint doi:10.5705/ss.202020.0440