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Targeted learning ensembles for optimal individualized treatment rules with time-to-event outcomes

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  • I Díaz
  • O Savenkov
  • K Ballman

Abstract

SummaryWe consider estimation of an optimal individualized treatment rule when a high-dimensional vector of baseline variables is available. Our optimality criterion is with respect to delaying the expected time to occurrence of an event of interest. We use semiparametric efficiency theory to construct estimators with properties such as double robustness. We propose two estimators of the optimal rule, which arise from considering two loss functions aimed at directly estimating the conditional treatment effect and recasting the problem in terms of weighted classification using the 0-1 loss function. Our estimated rules are ensembles that minimize the crossvalidated risk of a linear combination in a user-supplied library of candidate estimators. We prove oracle inequalities bounding the finite-sample excess risk of the estimator. The bounds depend on the excess risk of the oracle selector and a doubly robust term related to estimation of the nuisance parameters. We discuss the convergence rates of our estimator to the oracle selector, and illustrate our methods by analysis of a phase III randomized study testing the efficacy of a new therapy for the treatment of breast cancer.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:723-738.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy017
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    References listed on IDEAS

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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. Kara E. Rudolph & Iván Díaz, 2022. "When the ends do not justify the means: Learning who is predicted to have harmful indirect effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 573-589, December.
    3. Yiyi Huo & Yingying Fan & Fang Han, 2023. "On the adaptation of causal forests to manifold data," Papers 2311.16486, arXiv.org, revised Dec 2023.
    4. 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.

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