A two-state Markov chain for heterogeneous transitional data: a quasi-likelihood approach

Area of Science:

• Biostatistics
• Epidemiology
• Chronic Disease Research

Background:

• Chronic diseases often involve binary outcomes, with scientific interest focused on transitions between disease states.
• Disease progression is frequently heterogeneous, complicating accurate inference on transition processes.
• Existing models struggle to adequately capture individual variability in disease activity.

Purpose of the Study:

• To present a novel statistical model that incorporates subject-level heterogeneity in transition probabilities for chronic diseases.
• To develop a generalized estimating equations (GEE) approach for estimating parameters in a two-state Markov chain model with random transition probabilities.
• To extend the methodology for estimating derived transition matrix quantities and incorporating covariate dependence.

Main Methods:

• A quasi-likelihood formulation for a two-state Markov chain is proposed, specifying the first two moments of the transition probability distribution.
• Generalized estimating equations (GEE) are developed for estimating the mean and variance of the random transition probabilities.
• The methodology is applied to respiratory illness data in children with intrauterine growth retardation and validated through simulation studies.

Main Results:

• The proposed model effectively incorporates heterogeneity, allowing transition probabilities to vary randomly across subjects.
• The GEE approach provides robust estimation of model parameters and derived quantities like expected first passage times.
• Simulation results demonstrate the procedure's finite sample properties and highlight significant bias when heterogeneity is ignored.

Conclusions:

• The developed statistical framework offers a powerful tool for analyzing disease transition patterns in the presence of unobserved heterogeneity.
• Accurate modeling of individual variability is crucial for reliable inference on disease progression and for avoiding biased results.
• The methodology has practical applications in summarizing disease transition patterns and can be extended to include covariate effects.