IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v18y2022i1p243-262n11.html
   My bibliography  Save this article

Estimation of semi-Markov multi-state models: a comparison of the sojourn times and transition intensities approaches

Author

Listed:
  • Asanjarani Azam

    (The University of Auckland, Auckland, New Zealand)

  • Liquet Benoit

    (Department of Mathematics and Statistics, Macquarie University, Université de Pau et des Pays de l'Adour, E2S-UPPA, Pau, France)

  • Nazarathy Yoni

    (The University of Queensland, Brisbane, Australia)

Abstract

Semi-Markov models are widely used for survival analysis and reliability analysis. In general, there are two competing parameterizations and each entails its own interpretation and inference properties. On the one hand, a semi-Markov process can be defined based on the distribution of sojourn times, often via hazard rates, together with transition probabilities of an embedded Markov chain. On the other hand, intensity transition functions may be used, often referred to as the hazard rates of the semi-Markov process. We summarize and contrast these two parameterizations both from a probabilistic and an inference perspective, and we highlight relationships between the two approaches. In general, the intensity transition based approach allows the likelihood to be split into likelihoods of two-state models having fewer parameters, allowing efficient computation and usage of many survival analysis tools. Nevertheless, in certain cases the sojourn time based approach is natural and has been exploited extensively in applications. In contrasting the two approaches and contemporary relevant R packages used for inference, we use two real datasets highlighting the probabilistic and inference properties of each approach. This analysis is accompanied by an R vignette.

Suggested Citation

  • Asanjarani Azam & Liquet Benoit & Nazarathy Yoni, 2022. "Estimation of semi-Markov multi-state models: a comparison of the sojourn times and transition intensities approaches," The International Journal of Biostatistics, De Gruyter, vol. 18(1), pages 243-262, May.
    • Handle: RePEc:bpj:ijbist:v:18:y:2022:i:1:p:243-262:n:11
    DOI: 10.1515/ijb-2020-0083
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2020-0083
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2020-0083?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. Pierre Joly & Daniel Commenges, 1999. "A Penalized Likelihood Approach for a Progressive Three-State Model with Censored and Truncated Data: Application to AIDS," Biometrics, The International Biometric Society, vol. 55(3), pages 887-890, September.
    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. Andrew C. Titman & Linda D. Sharples, 2010. "Semi-Markov Models with Phase-Type Sojourn Distributions," Biometrics, The International Biometric Society, vol. 66(3), pages 742-752, September.
    2. Li, Chenxi, 2016. "Cause-specific hazard regression for competing risks data under interval censoring and left truncation," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 197-208.
    3. Proust-Lima, Cécile & Joly, Pierre & Dartigues, Jean-François & Jacqmin-Gadda, Hélène, 2009. "Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1142-1154, February.
    4. Marc Chadeau‐Hyam & Paul S. Clarke & Chantal Guihenneuc‐Jouyaux & Simon N. Cousens & Robert G. Will & Azra C. Ghani, 2010. "An application of hidden Markov models to the French variant Creutzfeldt–Jakob disease epidemic," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 839-853, November.
    5. B. A. Griffin & S. W. Lagakos, 2008. "Design and Analysis of Arm-in-Cage Experiments: Inference for Three-State Progressive Disease Models with Common Periodic Observation Times," Biometrics, The International Biometric Society, vol. 64(2), pages 337-344, June.
    6. David B. Dunson & Donna D. Baird, 2001. "A Flexible Parametric Model for Combining Current Status and Age at First Diagnosis Data," Biometrics, The International Biometric Society, vol. 57(2), pages 396-403, June.
    7. Machado, Robson J.M. & van den Hout, Ardo & Marra, Giampiero, 2021. "Penalised maximum likelihood estimation in multi-state models for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    8. E. Mathieu & Y. Foucher & P. Dellamonica & J. P. Daures, 2007. "Parametric and Non Homogeneous Semi-Markov Process for HIV Control," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 389-397, September.
    9. Andrew C. Titman, 2011. "Flexible Nonhomogeneous Markov Models for Panel Observed Data," Biometrics, The International Biometric Society, vol. 67(3), pages 780-787, September.

    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:bpj:ijbist:v:18:y:2022:i:1:p:243-262:n:11. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.