Covariate adjustment in randomized experiments with missing outcomes and covariates
研究了随机实验中结果和协变量缺失时，回归调整和倾向得分加权两种协变量调整方法的效率差异，并推荐了在不同情况下的选择策略。
Summary Covariate adjustment can improve precision in analysing randomized experiments. With fully observed data, regression adjustment and propensity score weighting are asymptotically equivalent in improving efficiency over unadjusted analysis. When some outcomes are missing, we consider combining these two adjustment methods with the inverse probability of observation weighting for handling missing outcomes, and show that the equivalence between the two methods breaks down. Regression adjustment no longer ensures efficiency gain over unadjusted analysis unless the true outcome model is linear in covariates or the outcomes are missing completely at random. Propensity score weighting, in contrast, still guarantees efficiency over unadjusted analysis, and including more covariates in adjustment never harms asymptotic efficiency. Moreover, we establish the value of using partially observed covariates to secure additional efficiency by the missingness indicator method, which imputes all missing covariates by zero and uses the union of the completed covariates and corresponding missingness indicators as the new, fully observed covariates. Based on these findings, we recommend using regression adjustment in combination with the missingness indicator method if the linear outcome model or missing-completely-at-random assumption is plausible and using propensity score weighting with the missingness indicator method otherwise.