BOUNDS ON THE CONDITIONAL AND AVERAGE TREATMENT EFFECT WITH UNOBSERVED CONFOUNDING FACTORS

• 成果类型: Article
• 署名作者: Yadlowsky, Steve; Namkoong, Hongseok; Basu, Sanjay; Duchi, John; Tian, Lu
• 署名单位: Alphabet Inc.; Google Incorporated; Columbia University; Stanford University; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2195
• 发表日期: 2022
• 页码: 2587-2615
• 关键词: superior design sensitivity; Asymptotic Normality; convergence-rates; estimators; probabilities; adjustment; exogeneity; variance

摘要

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semiparametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the op(n(-1/4)) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.