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Robust regression for optimal individualized treatment rules
Author(s) -
Xiao W.,
Zhang H. H.,
Lu W.
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8102
Subject(s) - estimator , outlier , quantile , computer science , consistency (knowledge bases) , quantile regression , robust statistics , robust regression , econometrics , asymptotic distribution , regression , conditional expectation , outcome (game theory) , statistics , mathematical optimization , mathematics , machine learning , artificial intelligence , mathematical economics
Because different patients may respond quite differently to the same drug or treatment, there is an increasing interest in discovering individualized treatment rules. In particular, there is an emerging need to find optimal individualized treatment rules, which would lead to the “best” clinical outcome. In this paper, we propose a new class of loss functions and estimators based on robust regression to estimate the optimal individualized treatment rules. Compared to existing estimation methods in the literature, the new estimators are novel and advantageous in the following aspects. First, they are robust against skewed, heterogeneous, heavy‐tailed errors or outliers in data. Second, they are robust against a misspecification of the baseline function. Third, under some general situations, the new estimator coupled with the pinball loss approximately maximizes the outcome's conditional quantile instead of the conditional mean, which leads to a more robust optimal individualized treatment rule than the traditional mean‐based estimators. 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 set.