Partial Identification of Causal Effects Using Proxy Variables
利用代理变量对因果效应进行部分识别AI 解读 ↓
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利用代理变量对因果效应进行部分识别
- 研究问题
- 存在未观测混杂而代理变量不足以满足完备性或识别桥函数时，能否仍从代理信息中获得因果效应的有用上下界并开展推断？
- 方法与思路
- 作者绕过完备性与桥函数识别构造效应界，再以 LogSumExp 平滑非光滑界泛函，推导有效影响函数，并讨论解析方差与自助法推断。
- 材料陈述的贡献
- 摘要称代理变量在不足以支持点识别时仍可提供因果效应界，并把相应部分识别与平滑推断结果扩展到存在隐藏中介的相关情境。
- 阅读关注点
- 应核对替代完备性的其他假设、上下界是否尖锐、单类代理的适用情形，以及平滑参数对界宽度、逼近误差和区间覆盖的影响。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实。免除完备性不等于无需其他限制；摘要未说明界的具体公式及全部适用条件。
原文摘要
Proximal causal inference is a framework for evaluating the causal effects in the presence of unmeasured confounding. For point identification, it leverages a pair of proxy variables to identify a bridge function that matches the dependence of potential outcomes or treatment variables on the hidden factors to corresponding functions of observed proxies. Unique identification requires that proxies are sufficiently relevant for hidden factors, a requirement that has previously been formalized as a completeness condition. However, completeness is not empirically testable, and although a bridge function may be well-defined in a given setting, lack of completeness, sometimes manifested by availability of a single type of proxy, may severely limit prospects for identification of a bridge function and thus a causal effect; therefore, potentially restricting the application of the framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. We establish that proxies can be leveraged to obtain bounds on the causal effect even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. Our bounds are non-smooth functionals of the underlying distribution. For inference, we employ LogSumExp approximations that yield smooth lower and upper bounds, and we derive the efficient influence functions of the resulting bound functionals which enable analytic variance estimation, while bootstrap confidence intervals remain available for regular plug-in implementations. We further establish analogous results in related settings where identification hinges upon hidden mediators for which proxies are available, however such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect of interest.