Second-order Markov multistate models
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Mireia Besalú
[1]
;
Guadalupe Gómez Melis
[2]
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[1] Universitat de Barcelona
Universitat de Barcelona
Barcelona, España
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[2] Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya
Barcelona, España
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- Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 48, Nº. 2, 2024, págs. 209-234
- Idioma: inglés
- Enlaces
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Resumen
Multistate models are well developed for continuous and discrete times under a first order Markov assumption. Motivated by a cohort of COVID-19 patients, a multistate model was designed based on 14 transitions among 7 states of a patient. Since a preliminary analysis showed that the first-order Markov condition was not met for some transitions, we have developed a second-order Markov model where the future evolution not only depends on the state at the current time but also on the state at the preceding time. Under a discrete time analysis, assuming homogeneity and that past information is restricted to two consecutive times, we expanded the transition probability matrix and proposed an extension of the Chapman-Kolmogorov equations. We propose two estimators for the second-order transition probabilities and illustrate them within the cohort of COVID-19 patients.
