Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding
This addresses the challenge of personalized causal inference in real-world settings where unconfoundedness assumptions are often violated, offering a method to quantify uncertainty due to unobserved confounding.
The paper tackles the problem of estimating individual-level causal effects from observational data when unobserved confounders are present, developing a functional interval estimator that predicts bounds on these effects and proving it converges to the tightest possible bounds.
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.