Log-Linear Model and Multistate Model to Assess the Rate of Fibrosis in Patients With NAFLD - Attia, Iman M. (Frontiers in Applied Mathematics and Statistics, 2022)
In this paper, the deleterious effects of obesity, type II diabetes, and insulin resistance, systolic and diastolic hypertension on the rate of progression of fibrosis in patients with non-alcoholic fatty liver disease (NAFLD) are illustrated using a new approach utilizing the Poisson regression to model the transition rate matrix. The observed counts in the transition count matrix are used as the 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 (CTMCs) followed by exponentiation of the estimated rate matrix to obtain the transition probability matrix at specific time points. A depicted, hypothetical, observational, prospective longitudinal study of 150 participants followed up every year for a total of 29 years recording their demographic characteristics and their timeline follow-up is demonstrated. The findings revealed that insulin resistance expressed by HOMA2-IR had the most deleterious effects among other factors on increasing the rate of fibrosis progression from state 1 to state 2, from state 2 to state 3, and from state 3 to state 4. The higher the level of HOMA2-IR is, the more rapid the rate of progression is. This analysis helps the health policymakers and medical insurance managers to allocate the financial and human resources for investigating and treating high-risk patients with NAFLD. In addition, this analysis can be used by pharmaceutical companies to conduct longitudinal studies to assess the effectiveness of the newly emerging anti-fibrotic drugs.