Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox

TL;DR

This paper develops a comprehensive framework for individualized decision-making under partial identification with unmeasured confounding, introducing a minimax optimal policy and revealing a paradox linking decision theory and confounding issues.

Contribution

It establishes a formal link between decision-making under partial identification and classical decision theory, and proposes a novel minimax optimal policy for such settings.

Findings

A formal connection between decision theory and partial identification.

A minimax solution minimizing maximum regret for decision policies.

Identification of a paradox linking decision-making and unmeasured confounding.

Abstract

Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification in a comprehensive manner. We establish a formal link between individualized decision-making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision-making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.