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

TL;DR

This paper introduces a novel cross-world imputation framework for handling missing baseline covariates in randomized controlled trials, demonstrating that existing methods like MIM are special cases and can achieve optimal efficiency.

Contribution

The paper proposes the cross-world imputation framework, unifying and extending existing methods for covariate imputation, and provides conditions for their efficiency equivalence.

Findings

MIM implicitly searches for optimal CWI values.

Single imputation can match MIM's efficiency under certain conditions.

CWI framework encompasses existing imputation strategies.

Abstract

In randomized controlled trials, adjusting for baseline covariates is often applied to improve the precision of treatment effect estimation. However, missingness in covariates is common. Recently, Zhao & Ding (2022) studied two simple strategies, the single imputation method and missingness indicator method (MIM), to deal with missing covariates, and showed that both methods can provide efficiency gain. To better understand and compare these two strategies, we propose and investigate a novel imputation framework termed cross-world imputation (CWI), which includes single imputation and MIM as special cases. 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.