Finding the optimal dynamic treatment regimes using smooth Fisher consistent surrogate loss
Nilanjana Laha, Aaron Sonabend-W, Rajarshi Mukherjee, Tianxi Cai
The Annals of Statistics · 2024 · Volume 52 · Issue 2
Abstract
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.
Keywords
classification, dynamic treatment regimes, empirical risk minimization, nonconvex optimization
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