Bounds on the conditional and average treatment effect with unobserved confounding factors

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 conditional average effect (CATE) confounders have bounded odds ratio selection. Our is scalable and allows flexible use model classes in estimation, including nonparametric black-box machine learning methods. Based these CATE, propose analysis (ATE). semiparametric estimator extends/bounds augmented inverse propensity weighted (AIPW) ATE under confounding. By constructing Neyman orthogonal score, our bound regular root-n so long as nuisance parameters are estimated at op(n−1/4) rate. complement methodology with optimality results showing that proposed tight certain cases. demonstrate method simulated real data examples, show accurate coverage confidence intervals practical finite sample regimes rich covariate information.