# Personalized Two-sided Dose Interval

## TL;DR

This paper introduces a novel, theoretically justified method for estimating personalized two-sided dose intervals that are robust and outperform existing approaches, with applications in medicine and social sciences.

## Contribution

It proposes a direct empirical risk minimization approach with a new loss function for personalized dose intervals, eliminating iterative procedures and ensuring statistical robustness.

## Key findings

- Method outperforms existing approaches in simulations.
- Loss function is doubly-robust to misspecification.
- Applications include warfarin dosing and social program analysis.

## Abstract

In fields such as medicine and social sciences, the goal of treatment is often to maintain the outcome of interest within a desirable range rather than to optimize its value. To achieve this, it may be more practical to recommend a treatment dose interval rather than a single fixed level for a study unit. Since individuals may respond differently to the same treatment level, the recommended dose interval should be personalized based on their unique characteristics. Iterative procedures have been proposed to jointly learn the lower and upper bounds of personalized dose intervals, but they lack theoretical justification. To fill this gap, we propose a method to learn personalized two-sided dose intervals based on empirical risk minimization using a novel loss function. The proposed loss function is designed to be well-defined over a tensor product function space, eliminating the need for iterative procedures. In addition, the loss function is doubly-robust to the misspecification of nuisance functions. We establish statistical properties of the estimated dose interval in terms of excess risk by leveraging the reproducing kernel Hilbert space theory. Our simulation study and real-world applications in warfarin dosing and the Job Corps program show that our proposed direct estimation method outperforms competing methods, including indirect regression-based methods.