الفهرس 
Analysis of chronic Diseases Progression Using Stochastic Models
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Abstract
Epidemiology is the science that studies the occurrence of the disease. Numerous mathematical methods can analyze such diseases. Multistate models are one of these mathematical methods that rely on solving differential equations to get some of the statistical indices that describe the process of the disease. Thus multistate Markov model is a valuable tool to model event data obtained from longitudinal studies. In medical research, this technique can model disease evolution in which each patient starts in one initial state and eventually ends in an absorbing or final one. Continuous-Time Markov Chain (CTMC) is one of these multistate models. CTMCs can estimate transition intensities and probabilities between states, state probability distribution at a specific time point, mean sojourn time in each state, life expectancy for the patient, and the expected number of patients in each state. As the prevalence of obesity and type 2 diabetes has reached epidemic levels that parallel the rates of the widely distributed non-alcoholic fatty liver disease (NAFLD), CTMC can model NAFLD to get better insight into the behavior of such a worldwide prevalent disease. CTMC helps improve the detection and treatment of NAFLD stages to avoid morbid complications.
This work provides a new approach using maximum likelihood estimation (MLE) to predict the transition rates among states. Once the rates are estimated, the transition probability matrix can be estimated. This approach compensates for the missing values when patients do not commit to the follow-up schedule by predicting the rate in each interval and taking weight from each rate corresponding to the proportion of transition counts in each interval in relation to the total transition counts.
The ”health, disease, and death” model is the simplest form of the CTMCs to study disease evolution. CTMC can model the expanded form of the disease constituting the nine states. Each disease process has its unique stages and specific transitions among the states. Also, a subset of the ”nine states model” that defines the early reversible stages of the disease, pointing to how the fibrosis evolves, was utilized to understand the factors that determine its existence, as fibrosis is the ominous predictor of bad outcomes and death. The results have yielded that the observed rates approximately equal the estimated rates obtained by MLE, as was the case when analyzing the simplest and the expanded models. Exponentiation of the estimated rate matrix yielded The transition probability matrix. The researcher used Poisson regression to relate these rates with the covariate risk factors of the disease like age, body mass index (BMI), homeostasis measurement assessment-insulin resistance (HOMA2-IR) reflecting insulin resistance, low-density lipoprotein cholesterol (LDL-Chol), systolic, and diastolic blood pressure. The study results were that insulin resistance was the most detrimental risk factor for disease progression. The more resistant to insulin the cells were, the higher the transition rate to advanced liver fibrosis was. The study contains hypothetical data for each model to highlight the statistical concepts used to analyze such a widely spread disease