To Adjust or not to Adjust? Estimating the Average Treatment Effect in Randomized Experiments with Missing Covariates
调整还是不调整？协变量缺失时随机实验平均处理效应的估计AI 解读 ↓
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调整还是不调整？协变量缺失时随机实验平均处理效应的估计
- 研究问题
- 随机实验中，除完整观测的处理前协变量外，是否还应调整存在缺失的协变量，以及如何利用缺失信息提高估计效率？
- 方法与思路
- 作者在设计型推断框架下比较调整策略；当缺失不受处理影响时，将缺失指示变量纳入回归调整，并提出若干修正。
- 材料陈述的贡献
- 摘要强调缺失指示变量可作为完整观测的处理前协变量，推荐缺失指示法，并从渐近与有限样本角度讨论其修改。
- 阅读关注点
- 应核对缺失不受处理影响的条件、缺失值在回归中的具体处理，以及各调整方法的效率结论和有限样本修正依据。
- 阅读边界
- 依据arXiv 2108.00152v1预印本摘要，不能据此声称该版本已经同行评审或期刊接收；具体效率比较和修正公式未说明。
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.