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Phase-type models for competing risks, with emphasis on identifiability issues

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  • Bo Henry Lindqvist

    (Norwegian University of Science and Technology)

Abstract

We first review some main results for phase-type distributions, including a discussion of Coxian distributions and their canonical representations. We then consider the extension of phase-type modeling to cover competing risks. This extension involves the consideration of finite state Markov chains with more than one absorbing state, letting each absorbing state correspond to a particular risk. The non-uniqueness of Markov chain representations of phase-type distributions is well known. In the paper we study corresponding issues for the competing risks case with the aim of obtaining identifiable parameterizations. Statistical inference for the Coxian competing risks model is briefly discussed and some real data are analyzed for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:2:d:10.1007_s10985-022-09547-7
    DOI: 10.1007/s10985-022-09547-7
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    References listed on IDEAS

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    1. Mogens Bladt & Antonio Gonzalez & Steffen L. Lauritzen, 2003. "The estimation of phase-type related functionals using Markov chain Monte Carlo methods," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(4), pages 280-300.
    2. 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.
    3. McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    4. Chantal Guihenneuc-Jouyaux & Sylvia Richardson & Ira M. Longini Jr., 2000. "Modeling Markers of Disease Progression by a Hidden Markov Process: Application to Characterizing CD4 Cell Decline," Biometrics, The International Biometric Society, vol. 56(3), pages 733-741, September.
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