  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.
