Optimal Treatment Regimes for Proximal Causal Learning

TL;DR

This paper introduces a new method for determining optimal individualized treatment strategies using proximal causal inference, addressing unmeasured confounding with proxy variables, and demonstrates its superiority through theory and experiments.

Contribution

It proposes a novel optimal treatment regime leveraging outcome and treatment confounding bridges within the proximal causal inference framework, with theoretical guarantees and practical validation.

Findings

The new regime outperforms existing methods in value function.

Theoretical guarantees include identification and consistency.

Numerical and real data experiments validate the approach.

Abstract

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.