Sharp Bounds for Continuous-Valued Treatment Effects with Unobserved Confounders

TL;DR

This paper develops sharp bounds and confidence intervals for continuous treatment effects in observational studies by relaxing unconfoundedness, providing more realistic and computationally efficient sensitivity analysis tools.

Contribution

It introduces novel sharp bounds for treatment effects under a continuous sensitivity model and proposes a doubly robust estimator, improving accuracy and efficiency over existing methods.

Findings

Sharper bounds than previous methods

Good coverage of true APO in simulations and real data

Reduced computation times compared to prior approaches

Abstract

In causal inference, treatment effects are typically estimated under the ignorability, or unconfoundedness, assumption, which is often unrealistic in observational data. By relaxing this assumption and conducting a sensitivity analysis, we introduce novel bounds and derive confidence intervals for the Average Potential Outcome (APO) - a standard metric for evaluating continuous-valued treatment or exposure effects. We demonstrate that these bounds are sharp under a continuous sensitivity model, in the sense that they give the smallest possible interval under this model, and propose a doubly robust version of our estimators. In a comparative analysis with the method of Jesson et al. (2022) (arXiv:2204.10022), using both simulated and real datasets, we show that our approach not only yields sharper bounds but also achieves good coverage of the true APO, with significantly reduced computation times.