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

Author

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  • 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
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    References listed on IDEAS

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    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.
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