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Optimal Individualized Treatments in Resource-Limited Settings

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  • Luedtke Alexander R.

    (Division of Biostatistics, University of California, 101 Haviland Hall, Berkeley, California 94720–7358, USA)

  • van der Laan Mark J.

    (Division of Biostatistics, University of California, 101 Haviland Hall, Berkeley, California 94720–7358, USA)

Abstract

An individualized treatment rule (ITR) is a treatment rule which assigns treatments to individuals based on (a subset of) their measured covariates. An optimal ITR is the ITR which maximizes the population mean outcome. Previous works in this area have assumed that treatment is an unlimited resource so that the entire population can be treated if this strategy maximizes the population mean outcome. We consider optimal ITRs in settings where the treatment resource is limited so that there is a maximum proportion of the population which can be treated. We give a general closed-form expression for an optimal stochastic ITR in this resource-limited setting, and a closed-form expression for the optimal deterministic ITR under an additional assumption. We also present an estimator of the mean outcome under the optimal stochastic ITR in a large semiparametric model that at most places restrictions on the probability of treatment assignment given covariates. We give conditions under which our estimator is efficient among all regular and asymptotically linear estimators. All of our results are supported by simulations.

Suggested Citation

  • Luedtke Alexander R. & van der Laan Mark J., 2016. "Optimal Individualized Treatments in Resource-Limited Settings," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 283-303, May.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:283-303:n:3
    DOI: 10.1515/ijb-2015-0007
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    References listed on IDEAS

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    1. S. A. Murphy, 2003. "Optimal dynamic treatment regimes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 331-355, May.
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    Cited by:

    1. Erik Sverdrup & Han Wu & Susan Athey & Stefan Wager, 2023. "Qini Curves for Multi-Armed Treatment Rules," Papers 2306.11979, arXiv.org, revised Oct 2024.
    2. Yanqing Wang & Yingqi Zhao & Yingye Zheng, 2022. "Targeted Search for Individualized Clinical Decision Rules to Optimize Clinical Outcomes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 564-581, December.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Zhen Li & Jie Chen & Eric Laber & Fang Liu & Richard Baumgartner, 2023. "Optimal Treatment Regimes: A Review and Empirical Comparison," International Statistical Review, International Statistical Institute, vol. 91(3), pages 427-463, December.
    5. James Cussens & Julia Hatamyar & Vishalie Shah & Noemi Kreif, 2025. "Fast Learning of Optimal Policy Trees," Papers 2506.15435, arXiv.org.
    6. Aaron L. Sarvet & Kerollos N. Wanis & Jessica G. Young & Roberto Hernandez‐Alejandro & Mats J. Stensrud, 2023. "Longitudinal incremental propensity score interventions for limited resource settings," Biometrics, The International Biometric Society, vol. 79(4), pages 3418-3430, December.
    7. Victor Chernozhukov & Whitney K. Newey & Rahul Singh, 2022. "Automatic Debiased Machine Learning of Causal and Structural Effects," Econometrica, Econometric Society, vol. 90(3), pages 967-1027, May.
    8. Jelena Bradic & Victor Chernozhukov & Whitney K. Newey & Yinchu Zhu, 2019. "Minimax Semiparametric Learning With Approximate Sparsity," Papers 1912.12213, arXiv.org, revised Jul 2025.
    9. Yanqing Wang & Ying‐Qi Zhao & Yingye Zheng, 2020. "Learning‐based biomarker‐assisted rules for optimized clinical benefit under a risk constraint," Biometrics, The International Biometric Society, vol. 76(3), pages 853-862, September.
    10. Victor Chernozhukov & Whitney K. Newey & Victor Quintas-Martinez & Vasilis Syrgkanis, 2021. "Automatic Debiased Machine Learning via Riesz Regression," Papers 2104.14737, arXiv.org, revised Mar 2024.

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