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The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
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Related Experiment Video

Updated: Jul 9, 2026

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

Modeling nonhomogeneous Markov processes via time transformation.

R A Hubbard1, L Y T Inoue1, J R Fann2

  • 1Department of Biostatistics, University of Washington, Box 357232, Seattle, Washington 98195, U.S.A.

Biometrics
|December 1, 2007
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical method to model chronic disease progression, transforming nonhomogeneous Markov processes into homogeneous ones. This approach accurately captures time-dependent disease transition rates, improving disease progression analysis.

Related Experiment Videos

Last Updated: Jul 9, 2026

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

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.