IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i1d10.1007_s11009-020-09839-1.html
   My bibliography  Save this article

Competing Risks Modeling by Extended Phase-Type Semi-Markov Distributions

Author

Listed:
  • Brenda Garcia-Maya

    (Université de Technologie de Compiègne)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne)

  • Bo Henry Lindqvist

    (Norwegian University of Science and Technology)

Abstract

We present competing risks models within a semi-Markov process framework via the semi-Markov phase-type distribution. We consider semi-Markov processes in continuous and discrete time with a finite number of transient states and a finite number of absorbing states. Each absorbing state represents a failure mode (in system reliability) or a cause of death of an individual (in survival analysis). This is an extension of the continuous-time Markov competing risks model presented in Lindqvist and Kjølen (2018). We derive the joint distribution of the lifetime and the failure cause via the transition function of semi-Markov processes in continuous and discrete-time. Some examples are given for illustration.

Suggested Citation

  • Brenda Garcia-Maya & Nikolaos Limnios & Bo Henry Lindqvist, 2022. "Competing Risks Modeling by Extended Phase-Type Semi-Markov Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 309-319, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-020-09839-1
    DOI: 10.1007/s11009-020-09839-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09839-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09839-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bo Henry Lindqvist & Susanne Hodneland Kjølen, 2018. "Phase-Type Models and Their Extension to Competing Risks," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel & Alex Karagrigoriou (ed.), Recent Advances in Multi-state Systems Reliability, pages 107-120, Springer.
    2. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. María Luz Gámiz & Nikolaos Limnios & Mari Carmen Segovia-García, 2023. "The continuous-time hidden Markov model based on discretization. Properties of estimators and applications," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 525-550, October.
    2. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    3. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    4. Bo Henry Lindqvist, 2023. "Phase-type models for competing risks, with emphasis on identifiability issues," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 318-341, April.
    5. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    6. N. C. Caballé & I. T. Castro, 2019. "Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 255-290, March.
    7. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.
    8. Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    9. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.
    10. Guglielmo D'Amico, 2016. "Generalized semi-Markovian dividend discount model: risk and return," Papers 1605.02472, arXiv.org.
    11. Inma T Castro & Sophie Mercier, 2016. "Performance measures for a deteriorating system subject to imperfect maintenance and delayed repairs," Journal of Risk and Reliability, , vol. 230(4), pages 364-377, August.
    12. Delia Montoro-Cazorla & Rafael Pérez-Ocón & Alicia Pereira das Neves-Yedig, 2021. "A Longitudinal Study of the Bladder Cancer Applying a State-Space Model with Non-Exponential Staying Time in States," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    13. Wu, Xiaoyue & Hillston, Jane, 2015. "Mission reliability of semi-Markov systems under generalized operational time requirements," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 122-129.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-020-09839-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.