June 2024 Risk-aware restricted outcome learning for individualized treatment regimes of schizophrenia
Shuying Zhu, Weining Shen, Haoda Fu, Annie Qu
Author Affiliations +
Ann. Appl. Stat. 18(2): 1319-1336 (June 2024). DOI: 10.1214/23-AOAS1836


Schizophrenia is a severe mental disorder that distorts patients’ perception of reality, and its treatment with antipsychotics can lead to significant side effects. Despite the heterogeneity in patient responses to treatments, most existing studies on individualized treatment regimes only focus on optimizing treatment efficacy, disregarding potential negative effects. To fill this gap, we propose a restricted outcome weighted learning method that optimizes efficacy outcomes while adhering to individual-level negative effect constraints. Our method is developed for multistage treatment decision problems that include single-stage decision as a special case. We propose an efficient learning algorithm that utilizes the difference-of-convex algorithm and the Lagrange multiplier to solve nonconvex optimization with nonconvex risk constraints. We also establish theoretical properties, including Fisher consistency and strong duality results, for the proposed method. We apply our method to a clinical study to design effective schizophrenia treatment [Stroup et al. (Schizophr. Bull. 29 (2003) 15–31)] and find that our approach reduces side-effect risk by at least 22.5% and improves efficacy by at least 26.3% compared to competing methods. In addition, we discover that certain covariates, such as the PANSS score, clinician global impressions severity score, and BMI, have a significant impact on controlling side effects and determining optimal treatment recommendations. These results are valuable in identifying subgroups of patients who need special attention when prescribing more aggressive treatment plans.

Funding Statement

Qu’s research is supported by the National Science Foundation grant DMS-1952406 and 2210640. Shen’s research is supported by Simons Foundation Award 512620.


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Shuying Zhu. Weining Shen. Haoda Fu. Annie Qu. "Risk-aware restricted outcome learning for individualized treatment regimes of schizophrenia." Ann. Appl. Stat. 18 (2) 1319 - 1336, June 2024. https://doi.org/10.1214/23-AOAS1836


Received: 1 July 2022; Revised: 1 August 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1836

Keywords: dynamic treatment regimes , individualized treatment regimes , individual-level risk control , outcome weighted learning , restricted optimization , side effects

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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