Finite Markov chains with absorbing states and mis-specified random effects: application to cognitive data

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Stochastic Processes

Background:

• Finite Markov chains with absorbing states are crucial for analyzing longitudinal categorical data.
• Estimating transition probabilities with fixed and random effects is complex due to numerous parameters.

Purpose of the Study:

• To develop a robust method for estimating fixed and random effects in finite Markov chains with absorbing states.
• To improve the accuracy of random effect estimation for identifying high-risk individuals and disease progression.

Main Methods:

• Employed a marginal model for fixed effects estimation across various random effect distributions.
• Utilized an h-likelihood method for estimating random effects based on fixed effect estimates.
• Applied the approach to longitudinal cognitive data from the Nun Study.

Main Results:

• Fixed effects estimates demonstrated robustness across diverse assumptions.
• Random effects analysis showed sensitivity to mis-specified random effect distributions (e.g., AIC, Q-Q plots).
• The proposed method allows for verification of random effect assumptions and more accurate estimation.

Conclusions:

• The developed approach enhances the analysis of longitudinal data with absorbing states.
• Precisely estimated random effects aid in identifying individuals at high risk for absorbing states and determining disease progression rates.