Bayesian analyses of longitudinal binary data using Markov regression models of unknown order.

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal binary data analysis requires methods to model time-varying dependencies.
• Understanding autoregressive dependence is crucial for accurately interpreting such data.
• Previous models may not adequately capture evolving transition probabilities over time.

Purpose of the Study:

• To develop and present non-homogeneous Markov regression models of unknown order.
• To assess the duration of autoregressive dependence in longitudinal binary data.
• To apply these models to understand substance use progression in a cohort of American Indian children.

Main Methods:

• Utilized logistic regression to model time-evolving transition probabilities based on past outcomes and covariates.
• Treated unknown initial values of the binary process as latent variables.
• Employed a Bayesian variable selection approach with Gibbs sampling for estimating unknown initial values, model parameters, and transition order.
• Implemented the deviance information criterion (DIC) for comparison in determining transition order.

Main Results:

• The proposed Bayesian variable selection approach effectively estimates model parameters and transition orders for longitudinal binary data.
• The models successfully captured the dynamics of substance use progression in the studied cohort.
• Demonstrated the utility of non-homogeneous Markov models in assessing autoregressive dependence.

Conclusions:

• Non-homogeneous Markov regression models offer a robust framework for analyzing longitudinal binary data with time-varying dependencies.
• The Bayesian variable selection method provides an effective approach for model order determination.
• The findings have implications for understanding developmental trajectories and informing interventions, particularly in public health research.