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Bounds on the conditional and average treatment effect with unobserved confounding factors. (English) Zbl 07628833

Summary: 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 \({o_p}({n^{-1/4}})\) 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.

MSC:

62F03 Parametric hypothesis testing
62F30 Parametric inference under constraints
62H12 Estimation in multivariate analysis
62H15 Hypothesis testing in multivariate analysis

Software:

grf; XGBoost
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Full Text: DOI arXiv

References:

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