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In randomized controlled trials, adjusting for baseline covariates is oftenapplied to improve the precision of treatment effect estimation. However,missingness in covariates is common. Recently, Zhao & Ding (2022) studied twosimple strategies, the single imputation method and missingness indicatormethod (MIM), to deal with missing covariates, and showed that both methods canprovide efficiency gain. To better understand and compare these two strategies,we propose and investigate a novel imputation framework termed cross-worldimputation (CWI), which includes single imputation and MIM as special cases.Through the lens of CWI, we show that MIM implicitly searches for the optimalCWI values and thus achieves optimal efficiency. We also derive conditionsunder which the single imputation method, by searching for the optimal singleimputation values, can achieve the same efficiency as the MIM.

Adjusting for Incomplete Baseline Covariates in Randomized Controlled Trials: A Cross-World Imputation Framework