TY - JOUR
T1 - Robust regression for optimal individualized treatment rules
AU - Xiao, W.
AU - Zhang, H. H.
AU - Lu, W.
N1 - Funding Information:
This research is partly supported by the grants NSF CCF 1740858 and NIH P01CA142538.
PY - 2019/5/20
Y1 - 2019/5/20
N2 - 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.
AB - 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.
KW - optimal individualized treatment rules
KW - personalized medicine
KW - quantile regression
KW - robust regression
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U2 - 10.1002/sim.8102
DO - 10.1002/sim.8102
M3 - Article
C2 - 30740747
AN - SCOPUS:85061428300
VL - 38
SP - 2059
EP - 2073
JO - Statistics in Medicine
JF - Statistics in Medicine
SN - 0277-6715
IS - 11
ER -