Novel Approach of Multistate Markov Chains to Evaluate Progression in the Expanded Model of Non-alcoholic Fatty Liver Disease - Attia, Iman M. (Frontiers in Applied Mathematics and Statistics, 2022)
Global increase in prevalence of obesity and type 2 Diabetes is strongly connected to increase prevalence of non-alcoholic fatty liver disease (NAFLD) worldwide. In the present paper, progression of (NAFLD) process is modeled by Continuous time Markov chains (CTMC) with 9 states. Maximum likelihood is used to estimate the transition intensities among the states. Once the transition intensities are obtained the mean sojourn time and its variance are estimated as well as the state probability distribution and its asymptotic covariance matrix. A hypothetical example based on longitudinal study assessing patients with NAFLD in various stages is discussed .The mean time to absorption is estimated as well as the other above mentioned statistical indices are examined . In this paper MLE is utilized in a new approach to compensate for the missing values in the follow up period of patients evaluated in longitudinal studies.