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June 2018 High-dimensional $A$-learning for optimal dynamic treatment regimes
Chengchun Shi, Ailin Fan, Rui Song, Wenbin Lu
Ann. Statist. 46(3): 925-957 (June 2018). DOI: 10.1214/17-AOS1570


Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients’ responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such as patient’s genetic information, demographic characteristics, medical history and clinical measurements over time are available, but not all of them are necessary for making treatment decision. This makes variable selection an emerging need in precision medicine.

In this paper, we propose a penalized multi-stage $A$-learning for deriving the optimal dynamic treatment regime when the number of covariates is of the nonpolynomial (NP) order of the sample size. To preserve the double robustness property of the $A$-learning method, we adopt the Dantzig selector, which directly penalizes the A-leaning estimating equations. Oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established. Empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the STAR∗D study.


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Chengchun Shi. Ailin Fan. Rui Song. Wenbin Lu. "High-dimensional $A$-learning for optimal dynamic treatment regimes." Ann. Statist. 46 (3) 925 - 957, June 2018.


Received: 1 January 2016; Revised: 1 January 2017; Published: June 2018
First available in Project Euclid: 3 May 2018

zbMATH: 1398.62029
MathSciNet: MR3797992
Digital Object Identifier: 10.1214/17-AOS1570

Primary: 62C99
Secondary: 62J07

Rights: Copyright © 2018 Institute of Mathematical Statistics


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Vol.46 • No. 3 • June 2018
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