Analysis of chronic diseases progression using stochastic modeling

TL;DR

This paper applies stochastic multi-state models, specifically Continuous Time Markov Chains, to analyze the progression of fatty liver disease, providing estimates for transition probabilities, life expectancy, and the impact of risk factors.

Contribution

It introduces a detailed multi-state modeling approach for fatty liver disease progression, incorporating covariates and comparing solution methods for transition probabilities.

Findings

The probability transition matrix can be estimated via exponentiation or differential equations.

The model estimates life expectancy at each disease stage.

High-risk factors significantly influence disease progression rates.

Abstract

This book handles the fatty liver disease from the bio-statistical point of view . It discusses the disease process in the simple general form of health-disease-death multi-states model . Continuous Time Markov Chains are used to estimate the rate transition matrix utilizing the MLE and Quasi-Newton formula , once obtained , the probability transition matrix can be estimated by exponentiation of the rate matrix . The probability transition matrix can also be obtained by solving the forward Kolmogorov differential equations , which yields more stable solution than exponentiation of rate matrix. The disease process is expanded in 9 states model to explain the transition among the detailed stages of the disease process , in more elaborate form. The probability transition matrix is used to estimate the number of patients in each stage , this matrix along with the rate transition matrix , both are used to estimate life expectancy of patients is each stage. These statistical indices are of great value as they can help the health policy makers and medical insurance managers to allocate the resources for investigating and treating patients in different stages of the disease . This method is of a high potential value to be used in longitudinal studies conducted by the pharmaceutical companies to evaluate the effect of anti-fibrotic drugs used to treat patients within the initial stages of fibrosis . Poisson regression model is also used to relate the high risk covariates such as type 2 diabetes, hypercholesterolemia , obesity and hypertension with the rate of progression and evolution of the stages of the disease over time. The general model , the expanded model and the model with covariates are illustrated by artificial hypothetical examples to demonstrate the mathematical statistical indices .