To adjust or not to adjust? Estimating the average treatment effect in randomized experiments with missing covariates
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调整还是不调整：协变量缺失的随机实验中平均处理效应估计
- 研究问题
- 随机实验存在处理前协变量缺失时，是否仍应调整这些协变量，如何利用缺失模式在保持设计本位推断的同时提高估计效率？
- 方法与思路
- 作者在完全随机分配的设计本位框架下比较多种调整策略，将不受处理影响的缺失指标作为完整观测协变量，并提出方法修正。
- 材料陈述的贡献
- 摘要称，未调整均值差保持无偏，缺失指标可带来额外效率；作者推荐缺失指标法，并从渐近与有限样本角度提出修正。
- 阅读关注点
- 核对缺失不受处理影响的要求、缺失协变量的填补与回归形式、缺失指标提供效率增益的条件，以及各项修正的目的。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出修正细节及完整效率条件，不能推广至处理影响缺失的场景。
原文摘要
Complete randomization allows for consistent estimation of the average treatment effect based on the difference in means of the outcomes without strong modeling assumptions on the outcome-generating process. Appropriate use of the pretreatment covariates can further improve the estimation efficiency. However, missingness in covariates is common in experiments and raises an important question: should we adjust for covariates subject to missingness, and if so, how? The unadjusted difference in means is always unbiased. The complete-covariate analysis adjusts for all completely observed covariates and improves the efficiency of the difference in means if at least one completely observed covariate is predictive of the outcome. Then what is the additional gain of adjusting for covariates subject to missingness? A key insight is that the missingness indicators act as fully observed pretreatment covariates as long as missingness is not affected by the treatment, and can thus be used in covariate adjustment to bring additional estimation efficiency. This motivates adding the missingness indicators to the regression adjustment, yielding the missingness-indicator method as a well-known but not so popular strategy in the literature of missing data. We recommend it due to its many advantages. We also propose modifications to the missingness-indicator method based on asymptotic and finite-sample considerations. To reconcile the conflicting recommendations in the missing data literature, we analyze and compare various strategies for analyzing randomized experiments with missing covariates under the design-based framework. This framework treats randomization as the basis for inference and does not impose any modeling assumptions on the outcome-generating process and missing-data mechanism.