Treatment Choice with Nonlinear Regret

TL;DR

This paper introduces a novel approach to treatment decision-making by minimizing a nonlinear transformation of welfare regret, providing explicit formulas for optimal rules and extending decision theory to limit experiments.

Contribution

It develops a new framework for treatment choice based on nonlinear regret minimization, including closed-form solutions and applications to normal models.

Findings

Closed-form fractions for finite-sample Bayes and minimax rules.

Extension of the approach to limit experiments.

Application to normal regression and sample size calculation.

Abstract

The literature focuses on the mean of welfare regret, which can lead to undesirable treatment choice due to sensitivity to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favoring treatment. We apply our framework to a normal regression model and sample size calculation.