April 2024 Finding the optimal dynamic treatment regimes using smooth Fisher consistent surrogate loss
Nilanjana Laha, Aaron Sonabend-W, Rajarshi Mukherjee, Tianxi Cai
Author Affiliations +
Ann. Statist. 52(2): 679-707 (April 2024). DOI: 10.1214/24-AOS2363


Large health care data repositories such as electronic health records (EHR) open new opportunities to derive individualized treatment strategies for complicated diseases such as sepsis. In this paper, we consider the problem of estimating sequential treatment rules tailored to a patient’s individual characteristics, often referred to as dynamic treatment regimes (DTRs). Our main objective is to find the optimal DTR that maximizes a discontinuous value function through direct maximization of Fisher consistent surrogate loss functions. In this regard, we demonstrate that a large class of concave surrogates fails to be Fisher consistent—a behavior that differs from the classical binary classification problems. We further characterize a nonconcave family of Fisher consistent smooth surrogate functions, which is amenable to gradient-descent type optimization algorithms. Compared to the existing direct search approach under the support vector machine framework (J. Amer. Statist. Assoc. 110 (2015) 583–598), our proposed DTR estimation via surrogate loss optimization (DTRESLO) method is more computationally scalable to large sample sizes and allows for broader functional classes for treatment policies. We establish theoretical properties for our proposed DTR estimator and obtain a sharp upper bound on the regret corresponding to our DTRESLO method. The finite sample performance of our proposed estimator is evaluated through extensive simulations. We also illustrate the working principles and benefits of our method for estimating an optimal DTR for treating sepsis using EHR data from sepsis patients admitted to intensive care units.

Funding Statement

Rajarshi Mukherjee and Nilanjana Laha’s research was supported by National Institutes of Health Grant P42ES030990.
Nilanjana Laha’s research was also supported by National Science Foundation Grant DMS-2311098.
Tianxi Cai’s research was supported by National Institutes of Health Grant R01LM013614.
Aaron Sonabend’s research was supported by the Boehringer–Ingelheim Fellowship at Harvard.


The third and the fourth authors are equal contributors.


Download Citation

Nilanjana Laha. Aaron Sonabend-W. Rajarshi Mukherjee. Tianxi Cai. "Finding the optimal dynamic treatment regimes using smooth Fisher consistent surrogate loss." Ann. Statist. 52 (2) 679 - 707, April 2024. https://doi.org/10.1214/24-AOS2363


Received: 1 May 2022; Revised: 1 August 2023; Published: April 2024
First available in Project Euclid: 9 May 2024

Digital Object Identifier: 10.1214/24-AOS2363

Keywords: ‎classification‎ , dynamic treatment regimes , empirical risk minimization , nonconvex optimization

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.52 • No. 2 • April 2024
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