Partial Identification of Causal Effects for Endogenous Continuous Treatments
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内生连续处理因果效应的部分识别
- 研究问题
- 在连续暴露可能存在未观测混杂时，如何扩展常见敏感性模型，识别反事实剂量反应曲线的界限并开展统计推断？
- 方法与思路
- 作者将 Rosenbaum 与边际敏感性模型的标量参数推广为暴露水平相关函数，建立统一伪结果回归及非参数界限估计。
- 材料陈述的贡献
- 摘要称估计具有二阶偏差，并在适当条件下获得一致性、收敛率及渐近正态性；另提供两模型的几何解释和二手烟应用。
- 阅读关注点
- 应核对敏感性函数的约束与实际含义、曲线界限的识别和锐利性，以及干扰参数学习、平滑选择与正态推断的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审与接收未核实；摘要未列出具体正则条件，效应界限取决于用户设定的内生性限制。
原文摘要
No unmeasured confounding is a common assumption when reasoning about counterfactual outcomes, but such an assumption may not be plausible in observational studies. Sensitivity analysis is often employed to assess the robustness of causal conclusions to unmeasured confounding, but existing methods are predominantly designed for binary treatments. In this paper, we provide natural extensions of two extensively used sensitivity frameworks -- the Rosenbaum and Marginal sensitivity models -- to the setting of continuous exposures. Our generalization replaces scalar sensitivity parameters with sensitivity functions that vary with exposure level, enabling richer modeling and sharper identification bounds. We develop a unified pseudo-outcome regression formulation for bounding the counterfactual dose-response curve under both models, and propose corresponding nonparametric estimators which have second order bias. These estimators accommodate modern machine learning methods for obtaining nuisance parameter estimators, which are shown to achieve $L^2$- consistency, minimax rates of convergence under suitable conditions. Our resulting estimators of bounds for the counterfactual dose-response curve are shown to be consistent and asymptotic normal allowing for a user-specified bound on the degree of uncontrolled exposure endogeneity. We also offer a geometric interpretation that relates the Rosenbaum and Marginal sensitivity model and guides their practical usage in global versus targeted sensitivity analysis. The methods are validated through simulations and a real-data application on the effect of second-hand smoke exposure on blood lead levels in children.