Name: Second Order Markov multistate models
Keywords: multistate models, Estadística matemàtica, Classificació AMS::62 Statistics::62J Linear inference, 330, Multistate models, Classificació AMS::62 Statistics::62N Survival analysis and censored data, 62M09, 62N02, 60J10, Classificació AMS::62 Statistics::62J Linear inference, regression, COVID-19, Mathematics - Statistics Theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2023Embargo end date: 01 Jan 2023Publisher:arXiv

Authors: Besalú Mayol, Mireia; Gómez Melis, Guadalupe;

doi: 10.48550/arxiv.2304.07837

arXiv: http://arxiv.org/abs/2304.07837

handle: 2117/418045 , 2117/421587

Second Order Markov multistate models

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Abstract

Multistate models are well developed for continuous and discrete times under a frstorder 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 frst-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.

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Keywords

multistate models, Estadística matemàtica, Classificació AMS::62 Statistics::62J Linear inference, 330, Multistate models, Classificació AMS::62 Statistics::62N Survival analysis and censored data, 62M09, 62N02, 60J10, Classificació AMS::62 Statistics::62J Linear inference, regression, COVID-19, Mathematics - Statistics Theory, Statistics Theory (math.ST), Non-Markov, 510, Mathematical statistics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica, Classificació AMS::62 Statistics::62M Inference from stochastic processes, FOS: Mathematics, regression, non-Markov

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