Robust regression for optimal individualized treatment rules

TL;DR

This paper introduces robust regression estimators for identifying optimal individualized treatment rules, capable of handling outliers and model misspecification, and can target conditional quantiles instead of means, improving treatment personalization.

Contribution

The paper proposes novel robust regression estimators for optimal treatment rules that are resilient to outliers and misspecification, and can optimize conditional quantiles rather than means.

Findings

Estimators are robust against heavy-tailed errors and outliers.

The proposed method can approximate conditional quantile maximization.

Empirical results demonstrate superior performance in simulations and AIDS data analysis.

Abstract

Because different patients may response quite differently to the same drug or treatment, there is increasing interest in discovering individualized treatment rule. In particular, people are eager to find the optimal individualized treatment rules, which if followed by the whole patient population would lead to the "best" outcome. In this paper, we propose new estimators based on robust regression with general loss functions to estimate the optimal individualized treatment rules. The new estimators possess the following nice properties: first, they are robust against skewed, heterogeneous, heavy-tailed errors or outliers; second, they are robust against misspecification of the baseline function; third, under certain situations, the new estimator coupled with pinball loss approximately maximizes the outcome's conditional quantile instead of conditional mean, which leads to a different optimal individualized treatment rule comparing with traditional Q- and A-learning. Consistency and asymptotic normality of the proposed estimators are established. Their empirical performance is demonstrated via extensive simulation studies and an analysis of an AIDS data.