Adaptive Randomization via Mahalanobis Distance
Yichen Qin, Yang Li, Wei Ma, Haoyu Yang, Feifang Hu · Statistica Sinica · 2022
In comparative studies, balancing covariate is often one of the most important concerns.However, chance imbalance still exists in many randomized experiments and it often becomes more serious as the number of covariates increases.To address this issue, we introduce a new randomization procedure, namely adaptive randomization via Mahalanobis distance (ARM).The proposed method allocates the units sequentially and adaptively, using the 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, estimation accuracy, hypothesis testing power, and computational time, for which we have established both theoretical results and numerical comparisons.More importantly, the proposed method attains the optimal covariate balance, in the sense that the estimated treatment effect under the proposed method attains its 1 Statistica Sinica: Newly accepted Paper (accepted