Causal Inference with a Hidden Treatment
真实处理不可观测时的因果推断AI 解读 ↓
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真实处理不可观测时的因果推断
- 研究问题
- 当真实处理始终不可观测、只能获得含误差的代理测量时，如何识别和有效估计因果效应，并处理依赖隐含处理的辅助函数？
- 方法与思路
- 作者构造完整数据模型与观测数据模型之间的影响函数空间映射，推导效率界与多重稳健估计器，并提出迭代估计算法。
- 材料陈述的贡献
- 摘要称，该框架涵盖多种因果目标量，给出闭式观测数据影响函数和大样本性质，并以模拟及阿尔茨海默病研究展示应用。
- 阅读关注点
- 应核对代理测量识别条件、空间映射的成立要求、多重稳健性的具体组合，以及迭代算法和非参数辅助估计所需条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未说明代理变量条件、算法收敛细节或有限样本数值，不能直接套用。
原文摘要
In many causal inference settings, the treatment of interest is not directly observed; instead, one or more error-prone proxy measurements are available, creating a fundamental identification challenge. Building on identification methods for hidden treatments with proxies, we develop a general semiparametric framework for causal effect estimation that accommodates several common estimands. Hidden treatment models differ fundamentally from classical missing-data settings, where semiparametric theory relies on positivity requiring a nonzero probability of observing a complete case for each treatment value. Here this assumption fails by design because the true treatment is never observed, creating new challenges for semiparametric characterization and efficient estimation. To overcome these challenges, we develop a new semiparametric characterization for hidden treatment models by deriving a formal mapping between the orthogonal complement to the nuisance tangent space, which contains all influence functions for a causal functional in the oracle full-data model, and its counterpart in the observed hidden treatment model. This mapping gives closed-form observed-data influence functions and yields the semiparametric efficiency bound. It also leads to semiparametric efficient estimators with a new form of multiple robustness or mixed bias property, enabling inference with nonparametric nuisance estimators. A further challenge is that some nuisance functions depend on the hidden treatment, preventing direct use of standard nonparametric regression methods. We introduce an iterative estimation algorithm and establish its large-sample properties. Simulations demonstrate the finite-sample performance of the proposed estimators, and an application estimates the causal effect of Alzheimer's disease on hippocampal volume using data from the Alzheimer's Disease Neuroimaging Initiative.