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Modeling of semi-competing risks by means of first passage times of a stochastic process

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  • Beate Sildnes

    (Norwegian University of Science and Technology
    BearingPoint)

  • Bo Henry Lindqvist

    (Norwegian University of Science and Technology)

Abstract

In semi-competing risks one considers a terminal event, such as death of a person, and a non-terminal event, such as disease recurrence. We present a model where the time to the terminal event is the first passage time to a fixed level c in a stochastic process, while the time to the non-terminal event is represented by the first passage time of the same process to a stochastic threshold S, assumed to be independent of the stochastic process. In order to be explicit, we let the stochastic process be a gamma process, but other processes with independent increments may alternatively be used. For semi-competing risks this appears to be a new modeling approach, being an alternative to traditional approaches based on illness-death models and copula models. In this paper we consider a fully parametric approach. The likelihood function is derived and statistical inference in the model is illustrated on both simulated and real data.

Suggested Citation

  • Beate Sildnes & Bo Henry Lindqvist, 2018. "Modeling of semi-competing risks by means of first passage times of a stochastic process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 153-175, January.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:1:d:10.1007_s10985-017-9399-y
    DOI: 10.1007/s10985-017-9399-y
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    References listed on IDEAS

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    1. Cooke, Roger M., 1993. "The total time on test statistic and age-dependent censoring," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 307-312, November.
    2. Jin‐Jian Hsieh & Weijing Wang & A. Adam Ding, 2008. "Regression analysis based on semicompeting risks data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 3-20, February.
    3. Andrés Christen, J. & Ruggeri, Fabrizio & Villa, Enrique, 2011. "Utility based maintenance analysis using a Random Sign censoring model," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 425-431.
    4. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    5. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    6. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
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    Cited by:

    1. Douglas E. Schaubel & Bin Nan, 2018. "Special issue dedicated to Jack Kalbfleisch," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 1-2, January.

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