Covariate adjustment can improve precision in analyzing 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 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 complete at random assumption is plausible and using propensity score weighting with the missingness indicator method otherwise.

翻译：协变量调整可提升随机实验分析的精度。当数据完全观测时，回归调整与倾向性得分加权在提升效率方面渐进等价于未调整分析。当存在结局缺失时，我们考虑将两种调整方法与逆观测概率加权结合以处理缺失结局，发现两种方法的等价性不再成立。除非真实结局模型为协变量线性或结局完全随机缺失，否则回归调整无法确保效率高于未调整分析。相比之下，倾向性得分加权仍能保证优于未调整分析的效率，且纳入更多协变量不会损害渐近效率。此外，我们建立了利用部分观测协变量通过缺失指示符方法获取额外效率的价值——该方法将所有缺失协变量填补为零，并将补全协变量与对应缺失指示符的并集作为新的完全观测协变量。基于这些发现，我们建议在假设线性结局模型或完全随机缺失成立时采用缺失指示符法结合回归调整，否则采用缺失指示符法结合倾向性得分加权。