Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding
Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding
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发表时间：
2018-10
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通讯作者：
Nathan Kallus;Xiaojie Mao;Angela Zhou
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作者：
Nathan Kallus;Xiaojie Mao;Angela Zhou
我们研究从存在未观测到的混杂因素的观测数据中学习条件平均处理效应（CATE）的问题。CATE函数将基线协变量映射到个体因果效应预测，它是个性化评估的关键。近期的研究工作集中在无混杂性（即不存在未观测到的混杂因素）的情况下如何学习CATE。由于当无混杂性假设被违反时，CATE可能无法被识别，我们开发了一种函数区间估计器，它能在无混杂性假设被实际违反的情况下预测个体因果效应的界限。我们的估计器采用加权核估计器的形式，其权重是对抗性变化的。我们证明了我们的估计器是精确的，即当可能存在未观测到的混杂因素时，它恰好收敛到CATE可能的最紧界限。此外，我们研究了从我们的估计器导出的个性化决策规则，并证明它们渐近地实现了最优的极小极大后悔值。我们在模拟研究中评估了我们的方法，并通过比较一项真实观测研究和临床试验的结论，展示了它在激素替代疗法案例中的应用。
We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, i.e., when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator takes the form of a weighted kernel estimator with weights that vary adversarially. We prove that our estimator is sharp in that it converges exactly to the tightest bounds possible on CATE when there may be unobserved confounders. Further, we study personalized decision rules derived from our estimator and prove that they achieve optimal minimax regret asymptotically. We assess our approach in a simulation study as well as demonstrate its application in the case of hormone replacement therapy by comparing conclusions from a real observational study and clinical trial.