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High-dimensional A-learning for optimal dynamic treatment regimes

Author

Listed:
  • Shi, Chengchun
  • Fan, Ailin
  • Song, Rui
  • Lu, Wenbin

Abstract

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.

Suggested Citation

  • Shi, Chengchun & Fan, Ailin & Song, Rui & Lu, Wenbin, 2018. "High-dimensional A-learning for optimal dynamic treatment regimes," LSE Research Online Documents on Economics 102113, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:102113
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    File URL: https://eprints.lse.ac.uk/102113/
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    Citations

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    Cited by:

    1. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    2. He, Yizeng & Kim, Soyoung & Kim, Mi-Ok & Saber, Wael & Ahn, Kwang Woo, 2021. "Optimal treatment regimes for competing risk data using doubly robust outcome weighted learning with bi-level variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    3. Shi, Chengchun & Luo, Shikai & Le, Yuan & Zhu, Hongtu & Song, Rui, 2022. "Statistically efficient advantage learning for offline reinforcement learning in infinite horizons," LSE Research Online Documents on Economics 115598, London School of Economics and Political Science, LSE Library.
    4. Cai, Hengrui & Shi, Chengchun & Song, Rui & Lu, Wenbin, 2023. "Jump interval-learning for individualized decision making with continuous treatments," LSE Research Online Documents on Economics 118231, London School of Economics and Political Science, LSE Library.
    5. Hyung Park & Thaddeus Tarpey & Eva Petkova & R. Todd Ogden, 2024. "A high-dimensional single-index regression for interactions between treatment and covariates," Statistical Papers, Springer, vol. 65(7), pages 4025-4056, September.
    6. Shi, Chengchun & Li, Lexin, 2022. "Testing mediation effects using logic of Boolean matrices," LSE Research Online Documents on Economics 108881, London School of Economics and Political Science, LSE Library.
    7. Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time with potential local projections," Papers 2103.01280, arXiv.org, revised Jan 2024.
    8. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    9. Shi, Chengchun & Zhang, Shengxing & Lu, Wenbin & Song, Rui, 2022. "Statistical inference of the value function for reinforcement learning in infinite-horizon settings," LSE Research Online Documents on Economics 110882, London School of Economics and Political Science, LSE Library.
    10. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.

    More about this item

    Keywords

    A-learning; Dantzig selector; model misspecification; NP-dimensionality; optimal dynamic treatment regime; oracle inequality;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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