Two-Part Hidden Semi-Markov Mixed Effects Models for Semi-Continuous Longitudinal Data

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Modeling dynamic heterogeneity is crucial for understanding individual changes over time.
• Analyzing semi-continuous longitudinal data presents challenges due to its mixed discrete and continuous nature.
• Existing methods struggle to fully capture the complexities of dynamic heterogeneity in such data.

Purpose of the Study:

• To develop a robust statistical model for dynamic heterogeneity in semi-continuous longitudinal data.
• To address the limitations of current methods in analyzing complex longitudinal trajectories.
• To accurately model both zero and positive outcomes within a unified framework.

Main Methods:

• Development of a two-part hidden semi-Markov mixed-effects model.
• Incorporation of a discrete binary indicator for zero outcomes and a continuous hidden semi-Markov model for positive values.
• Utilizing likelihood ratio test state iteration algorithms and Bayesian methods for parameter estimation.

Main Results:

• The proposed model effectively handles the semi-continuous nature of longitudinal responses.
• Demonstrated ability to reveal distinct longitudinal trajectories and dynamic heterogeneity.
• Successful application to the Health and Retirement Study dataset, validated by simulation studies.

Conclusions:

• The two-part hidden semi-Markov mixed-effects model offers a powerful approach for analyzing dynamic heterogeneity in semi-continuous longitudinal data.
• The methodology provides accurate state estimation and parameter estimation using Bayesian inference.
• This approach enhances the understanding of individual change patterns in complex datasets.