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

Asanjarani Azam (), Liquet Benoit () and Nazarathy Yoni ()
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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

The International Journal of Biostatistics, 2022, vol. 18, issue 1, 243-262

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.

Keywords: hazard rate; intensity transition; multi-state model; semi-Markov model; sojourn time (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/ijb-2020-0083

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