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Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results

Author

Listed:
  • Orellana Liliana

    (Instituto de Cálculo, Universidad de Buenos Aires)

  • Rotnitzky Andrea

    (Universidad Torcuato Di Tella and Harvard School of Public Health)

  • Robins James M.

    (Harvard School of Public Health)

Abstract

In this companion article to "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content" [Orellana, Rotnitzky and Robins (2010), IJB, Vol. 6, Iss. 2, Art. 7] we present (i) proofs of the claims in that paper, (ii) a proposal for the computation of a confidence set for the optimal index when this lies in a finite set, and (iii) an example to aid the interpretation of the positivity assumption.

Suggested Citation

  • Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-19, March.
    • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:2:n:9
    DOI: 10.2202/1557-4679.1242
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    Citations

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    Cited by:

    1. Q. Clairon & R. Henderson & N. J. Young & E. D. Wilson & C. J. Taylor, 2021. "Adaptive treatment and robust control," Biometrics, The International Biometric Society, vol. 77(1), pages 223-236, March.
    2. Lucia Babino & Andrea Rotnitzky & James Robins, 2019. "Multiple robust estimation of marginal structural mean models for unconstrained outcomes," Biometrics, The International Biometric Society, vol. 75(1), pages 90-99, March.
    3. Eric B. Laber & Anastasios A. Tsiatis & Marie Davidian & Shannon T. Holloway, 2014. "Discussion of “Combining biomarkers to optimize patient treatment recommendation”," Biometrics, The International Biometric Society, vol. 70(3), pages 707-710, September.
    4. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    5. Luedtke Alexander R. & van der Laan Mark J., 2016. "Super-Learning of an Optimal Dynamic Treatment Rule," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 305-332, May.
    6. Ying Huang & Youyi Fong, 2014. "Identifying optimal biomarker combinations for treatment selection via a robust kernel method," Biometrics, The International Biometric Society, vol. 70(4), pages 891-901, December.
    7. Shu Yang & Anastasios A. Tsiatis & Michael Blazing, 2018. "Modeling survival distribution as a function of time to treatment discontinuation: A dynamic treatment regime approach," Biometrics, The International Biometric Society, vol. 74(3), pages 900-909, September.
    8. Eric B. Laber & Daniel J. Lizotte & Bradley Ferguson, 2014. "Set-valued dynamic treatment regimes for competing outcomes," Biometrics, The International Biometric Society, vol. 70(1), pages 53-61, March.
    9. Baqun Zhang & Anastasios A. Tsiatis & Eric B. Laber & Marie Davidian, 2012. "A Robust Method for Estimating Optimal Treatment Regimes," Biometrics, The International Biometric Society, vol. 68(4), pages 1010-1018, December.
    10. Cain Lauren E. & Robins James M. & Lanoy Emilie & Logan Roger & Costagliola Dominique & Hernán Miguel A., 2010. "When to Start Treatment? A Systematic Approach to the Comparison of Dynamic Regimes Using Observational Data," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-26, April.
    11. Yasuhiro Hagiwara & Tomohiro Shinozaki & Hirofumi Mukai & Yutaka Matsuyama, 2021. "Sensitivity analysis for subsequent treatments in confirmatory oncology clinical trials: A two‐stage stochastic dynamic treatment regime approach," Biometrics, The International Biometric Society, vol. 77(2), pages 702-714, June.
    12. Yunan Wu & Lan Wang, 2021. "Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes," Biometrics, The International Biometric Society, vol. 77(2), pages 465-476, June.
    13. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2022. "Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals," Papers 2203.13887, arXiv.org, revised Jun 2023.
    14. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    15. Xiaofei Bai & Anastasios A. Tsiatis & Wenbin Lu & Rui Song, 2017. "Optimal treatment regimes for survival endpoints using a locally-efficient doubly-robust estimator from a classification perspective," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 585-604, October.
    16. 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.
    17. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-49, March.
    18. Ruoqing Zhu & Ying-Qi Zhao & Guanhua Chen & Shuangge Ma & Hongyu Zhao, 2017. "Greedy outcome weighted tree learning of optimal personalized treatment rules," Biometrics, The International Biometric Society, vol. 73(2), pages 391-400, June.
    19. Emily L. Butler & Eric B. Laber & Sonia M. Davis & Michael R. Kosorok, 2018. "Incorporating Patient Preferences into Estimation of Optimal Individualized Treatment Rules," Biometrics, The International Biometric Society, vol. 74(1), pages 18-26, March.
    20. Mélanie Prague & Daniel Commenges & Jon Michael Gran & Bruno Ledergerber & Jim Young & Hansjakob Furrer & Rodolphe Thiébaut, 2017. "Dynamic models for estimating the effect of HAART on CD4 in observational studies: Application to the Aquitaine Cohort and the Swiss HIV Cohort Study," Biometrics, The International Biometric Society, vol. 73(1), pages 294-304, March.
    21. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.

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