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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
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    References listed on IDEAS

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    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.
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