Second Order Markov multistate models

2023/04/16 by Mireia Besalú, Besalú, Mireia, Guadalupe Gómez Melis +1
Business, Management and Accounting · #60J10 #62M09 #62N02 #Advanced Queuing Theory Analysis #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2304.07837

openalex publication_date 2023/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Multistate models (MSM) are well developed for continuous and discrete times under a first order Markov assumption. Motivated by a cohort of COVID-19 patients, an MSM 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 current but also on the preceding state. Under a discrete time analysis, assuming homogeneity and that past information is restricted to 2 consecutive times, we expanded the transition probability matrix and proposed an extension of the Chapman- Kolmogorov equations.

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