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Super-Learning of an Optimal Dynamic Treatment Rule

Author

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  • Luedtke Alexander R.
  • van der Laan Mark J.

    (Division of Biostatistics, University of California, Berkeley, CA, USA)

Abstract

We consider the estimation of an optimal dynamic two time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to depend only on a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric, beyond possible knowledge about the treatment and censoring mechanisms. We propose data adaptive estimators of this optimal dynamic regime which are defined by sequential loss-based learning under both the blip function and weighted classification frameworks. Rather than a priori selecting an estimation framework and algorithm, we propose combining estimators from both frameworks using a super-learning based cross-validation selector that seeks to minimize an appropriate cross-validated risk. The resulting selector is guaranteed to asymptotically perform as well as the best convex combination of candidate algorithms in terms of loss-based dissimilarity under conditions. We offer simulation results to support our theoretical findings.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:305-332:n:18
    DOI: 10.1515/ijb-2015-0052
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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.
    2. Moodie, Erica E. M. & Platt, Robert W. & Kramer, Michael S., 2009. "Estimating Response-Maximized Decision Rules With Applications to Breastfeeding," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 155-165.
    3. Mark van der Laan & Sandrine Dudoit & Aad van der Vaart, 2004. "The Cross-Validated Adaptive Epsilon-Net Estimator," U.C. Berkeley Division of Biostatistics Working Paper Series 1141, Berkeley Electronic Press.
    4. 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.
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    Cited by:

    1. Jin Wang & Donglin Zeng & D. Y. Lin, 2022. "Semiparametric single-index models for optimal treatment regimens with censored outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 744-763, October.
    2. I Díaz & O Savenkov & K Ballman, 2018. "Targeted learning ensembles for optimal individualized treatment rules with time-to-event outcomes," Biometrika, Biometrika Trust, vol. 105(3), pages 723-738.
    3. Qingliang Fan & Yu-Chin Hsu & Robert P. Lieli & Yichong Zhang, 2022. "Estimation of Conditional Average Treatment Effects With High-Dimensional Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 313-327, January.

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