Jump Interval-Learning for Individualized Decision Making

TL;DR

This paper introduces jump interval-learning, a novel method for creating individualized interval-valued decision rules in continuous treatment settings, using jump penalized regression and dynamic programming.

Contribution

It develops a new approach for continuous treatments that produces flexible interval decisions, combining jump penalized regression with neural networks and dynamic programming.

Findings

The method effectively estimates optimal treatment intervals in simulations.

It demonstrates improved decision-making in a warfarin study.

Statistical properties are established for different outcome regression functions.

Abstract

An individualized decision rule (IDR) is a decision function that assigns each individual a given treatment based on his/her observed characteristics. Most of the existing works in the literature consider settings with binary or finitely many treatment options. In this paper, we focus on the continuous treatment setting and propose a jump interval-learning to develop an individualized interval-valued decision rule (I2DR) that maximizes the expected outcome. Unlike IDRs that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, making it more flexible to implement in practice. To derive an optimal I2DR, our jump interval-learning method estimates the conditional mean of the outcome given the treatment and the covariates via jump penalized regression, and derives the corresponding optimal I2DR based on the estimated outcome regression function. The regressor is allowed to be either linear for clear interpretation or deep neural network to model complex treatment-covariates interactions. To implement jump interval-learning, we develop a searching algorithm based on dynamic programming that efficiently computes the outcome regression function. Statistical properties of the resulting I2DR are established when the outcome regression function is either a piecewise or continuous function over the treatment space. We further develop a procedure to infer the mean outcome under the (estimated) optimal policy. Extensive simulations and a real data application to a warfarin study are conducted to demonstrate the empirical validity of the proposed I2DR.