Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding

TL;DR

This paper introduces a novel method for estimating bounds on individual causal effects in observational data with unobserved confounders, providing sharp estimates and optimal decision rules.

Contribution

It develops a functional interval estimator that predicts tight bounds on CATE under violations of unconfoundedness, with theoretical guarantees and practical applications.

Findings

Estimator converges to the tightest bounds on CATE.

Personalized decision rules achieve asymptotic optimal minimax regret.

Method performs well in simulations and real observational study.

Abstract

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.