发表机构
Toyo University（东洋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明平均处理效应的最优调整集性质源于其权重，并针对处理人群估计量推导效率界变化恒等式，证明无图最优准则，但无效应修饰时ATE最优集仍最优，并扩展至重叠权重等。
AI 中文摘要
图因果推断为平均处理效应的有效协变量调整提供了完整的理论：一个可由图计算的调整集，在每一个兼容分布下都是最优的。我们证明，这是平均处理效应的逆患病率权重的性质，而非一般因果估计量的性质。对于处理组平均处理效应，我们以调整集为索引给出效率界，并推导其在有效集的处理侧和结果侧扩展下变化的精确恒等式。仅预测处理组结果的协变量恰好是效率中性的，而预测对照组结果的协变量在倾向得分低于二分之一时可严格增大效率界——这是对补充引理的反转，其来源是一个对平均处理效应成立但对处理人群估计量失效的算术-几何平均不等式。一个图上的两个忠实分布的构造证明，对于处理人群估计量不存在图最优性准则；在无效应修饰下，ATE最优集在图形有效集中仍然是最优的，并有其优势的精确表达式。结果扩展到具有倾向依赖权重的加权平均处理效应，得到重叠权重的对称阈值、工具调整下的估计量漂移现象，以及常数权重是唯一使得结果侧补充从不增大效率界的光滑正权重的刻画。模拟和LaLonde数据提供了例证。
英文摘要
Graphical causal inference supplies a complete theory of efficient covariate adjustment for the average treatment effect: one adjustment set, computable from the graph, is optimal under every compatible distribution. We show that this is a property of the average treatment effect's inverse-prevalence weights, not of causal estimands in general. For the average treatment effect on the treated we index the efficiency bound by the adjustment set and derive exact identities for its change under treatment-side and outcome-side extensions of a valid set. Covariates that predict only the treated-arm outcome are exactly efficiency-neutral, and covariates that predict the control-arm outcome can strictly increase the bound when the propensity is below one half -- a reversal of the supplementation lemma whose source is an arithmetic-geometric-mean inequality that holds for the average treatment effect and fails for the treated-population estimand. A construction with two faithful distributions on one graph proves that no graphical optimality criterion exists for the treated-population estimand; under no effect modification the ATE-optimal set is nonetheless optimal among the graphically valid sets, with an exact expression for its advantage. The results extend to weighted average treatment effects with propensity-dependent weights, yielding symmetric thresholds for overlap weights, an estimand-drift phenomenon under instrument adjustment, and a characterization of constant weights as the only smooth positive weights for which outcome-side supplementation never increases the bound. Simulations and the LaLonde data provide illustrations.
Comments45 pages, 1 figure, 3 tables; proofs and numerical verification in the appendices. v2: states the 1 percent penalty threshold of the random-structure scan (Appendix B) and updates the replication archive to version 1.1. Replication code and data: https://github.com/sokubo/paper-estimand-adjustment-replication
