Resumen de Second-order Markov multistate models

Mireia Besalú Mayol, Guadalupe Gómez Melis

• 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.