Adjusting for incomplete baseline covariates in randomized controlled trials: a cross-world imputation framework

In randomized controlled trials, adjusting for baseline covariates is commonly used to improve the precision of treatment effect estimation. However, covariates often have missing values. Recently, Zhao and Ding studied two simple strategies, the single imputation method and missingness-indicator method (MIM), to handle missing covariates and showed that both methods can provide an efficiency gain compared to not adjusting for covariates. To better understand and compare these two strategies, we propose and investigate a novel theoretical imputation framework termed cross-world imputation (CWI). This framework includes both single imputation and MIM as special cases, facilitating the comparison of their efficiency. Through the lens of CWI, we show that MIM implicitly searches for the optimal CWI values and thus achieves optimal efficiency. We also derive conditions under which the single imputation method, by searching for the optimal single imputation values, can achieve the same efficiency as the MIM. We illustrate our findings through simulation studies and a real data analysis based on the Childhood Adenotonsillectomy Trial. We conclude by discussing the practical implications of our findings.