Balancing treatment assignment over all observed covariates in clinical trials

In practice it is very common for sets of covariate data to be incomplete, however, there is little work on balancing treatment assignment over partially observed covariates in literature. In this paper, we propose a new covariate-adaptive design to address this problem, which constructs imbalance measure by weighted absolute differences. Theoretical results show that overall imbalance, observed margin imbalance and fully observed stratum imbalance are all bounded in probability as the sample size increases, at the same time, restored margin imbalance and restored stratum imbalance increase with the rate n. Finally, we confirm theoretical findings and compare the proposed design with DBAI (Liu et al., 2015) through simulations.