Abstract
In the present paper, the deleterious effects of obesity, type 2diabetes and insulin resistance, systolic and diastolic hypertension on the rate of progression of fibrosis in non-alcoholic fatty liver disease (NAFLD) patients are illustrated using a new approach utilizing the Poisson regression to model the transition rate matrix. The observed counts in the transition counts matrix are used as response variables and the covariates are the risk factors for fatty liver. Then the estimated counts from running the Poisson regression are used to estimate the transition rates using the continuous time Markov chains (CTMC) followed by exponentiation of the estimated rate matrix to obtain the transition probability matrix at specific time points. Using a hypothetical data of 150 participants followed up every year for a total of 28 years recording their demographic characteristics and their timeline of follow up are demonstrated. The findings revealed that insulin resistance expressed by MOMA-IR 2 has the most deleterious effects among other factors for increasing the rate of forward progression of patients from state 1 to state 2 as well as from state 2 to state 3 and from state 3 to state 4. The higher the level of HOMA-IR is, the more rapid the rate of progression is.
Structural classification of continuous time Markov chains with applications
