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Tree-based modeling of time-varying coefficients in discrete time-to-event models

Author

Listed:
  • Marie-Therese Puth

    (University of Bonn
    University of Bonn)

  • Gerhard Tutz

    (Ludwig-Maximilians-University Munich)

  • Nils Heim

    (University Hospital Bonn)

  • Eva Münster

    (University of Bonn)

  • Matthias Schmid

    (University of Bonn)

  • Moritz Berger

    (University of Bonn)

Abstract

Hazard models are popular tools for the modeling of discrete time-to-event data. In particular two approaches for modeling time dependent effects are in common use. The more traditional one assumes a linear predictor with effects of explanatory variables being constant over time. The more flexible approach uses the class of semiparametric models that allow the effects of the explanatory variables to vary smoothly over time. The approach considered here is in between these modeling strategies. It assumes that the effects of the explanatory variables are piecewise constant. It allows, in particular, to evaluate at which time points the effect strength changes and is able to approximate quite complex variations of the change of effects in a simple way. A tree-based method is proposed for modeling the piecewise constant time-varying coefficients, which is embedded into the framework of varying-coefficient models. One important feature of the approach is that it automatically selects the relevant explanatory variables and no separate variable selection procedure is needed. The properties of the method are investigated in several simulation studies and its usefulness is demonstrated by considering two real-world applications.

Suggested Citation

  • Marie-Therese Puth & Gerhard Tutz & Nils Heim & Eva Münster & Matthias Schmid & Moritz Berger, 2020. "Tree-based modeling of time-varying coefficients in discrete time-to-event models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 545-572, July.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:3:d:10.1007_s10985-019-09489-7
    DOI: 10.1007/s10985-019-09489-7
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    References listed on IDEAS

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    1. Ronghui Xu & Sudeshna Adak, 2002. "Survival Analysis with Time-Varying Regression Effects Using a Tree-Based Approach," Biometrics, The International Biometric Society, vol. 58(2), pages 305-315, June.
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    5. Ruhe, Constantin, 2018. "Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses," Political Analysis, Cambridge University Press, vol. 26(1), pages 90-111, January.
    6. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460, Elsevier.
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    Cited by:

    1. Spuck, Nikolai & Schmid, Matthias & Monin, Malte & Berger, Moritz, 2025. "Confidence intervals for tree-structured varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 207(C).
    2. Alina Schenk & Moritz Berger & Matthias Schmid, 2024. "Pseudo-value regression trees," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(2), pages 439-471, April.

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