Modeling nonhomogeneous Markov processes via time transformation

Area of Science:

• Biostatistics
• Epidemiology
• Chronic Disease Research

Background:

• Longitudinal studies are crucial for understanding chronic disease progression using panel data.
• Markov process models are commonly used but often assume time homogeneity, which is frequently violated in real-world disease progression.
• Existing statistical tools for nonhomogeneous Markov processes are limited.

Purpose of the Study:

• To develop a novel statistical methodology for analyzing nonhomogeneous Markov processes in chronic disease progression.
• To address the limitations of time-homogeneous models by incorporating time-dependent transition rates.
• To provide a robust framework for estimating disease progression dynamics when transition rates vary over time.

Main Methods:

• Proposed transforming the time scale of nonhomogeneous Markov processes to an operational time scale, rendering the process homogeneous.
• Developed a joint estimation method for the time transformation and the transition intensity matrix.
• Assessed the maximum likelihood estimation via the Fisher scoring algorithm through simulation studies.
• Compared the proposed method against traditional homogeneous and piecewise homogeneous models.

Main Results:

• The proposed method effectively models nonhomogeneous disease progression by transforming the time scale.
• Simulation studies demonstrated the performance of the maximum likelihood estimation and Fisher scoring algorithm.
• The methodology successfully identified temporal trends in delirium incidence and recovery in stem cell transplantation recipients.

Conclusions:

• The developed method offers a powerful tool for analyzing chronic disease progression when transition rates are time-dependent.
• This approach enhances the understanding of disease dynamics by accurately capturing nonhomogeneity.
• The application to delirium progression highlights the practical utility of the method in clinical research.