GEAR: On Optimal Decision Making with Auxiliary Data

TL;DR

This paper introduces GEAR, a novel method that leverages auxiliary data to improve personalized decision making when primary outcomes are unobservable in the experimental sample, addressing long-term effect estimation challenges.

Contribution

GEAR is the first approach to incorporate auxiliary data for optimal decision rule estimation in the absence of primary outcomes in the experimental sample.

Findings

GEAR provides consistent estimators with desirable asymptotic properties.

Simulation studies confirm GEAR's effectiveness in practical scenarios.

Application to AIDS data demonstrates real-world utility.

Abstract

Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods usually require the primary outcome of interest in samples for assessing treatment effects, namely the experimental sample. However, in many studies, treatments may have a long-term effect, and as such the primary outcome of interest cannot be observed in the experimental sample due to the limited duration of experiments, which makes the estimation of ODR impossible. This paper is inspired to address this challenge by making use of an auxiliary sample to facilitate the estimation of ODR in the experimental sample. We propose an auGmented inverse propensity weighted Experimental and Auxiliary sample-based decision Rule (GEAR) by maximizing the augmented inverse propensity weighted value estimator over a class of decision rules using the experimental sample, with the primary outcome being imputed based on the auxiliary sample. The asymptotic properties of the proposed GEAR estimators and their associated value estimators are established. Simulation studies are conducted to demonstrate its empirical validity with a real AIDS application.