Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Quantile regression offers detailed distributional insights conditional on covariates.
• Existing methods for longitudinal data have limitations with temporal shocks and parameter heterogeneity.
• HIV progression data exemplifies challenges like sudden trend changes and individual-specific effects.

Purpose of the Study:

• To propose a novel quantile regression model for longitudinal continuous outcomes.
• To jointly model time-varying and time-constant random coefficients.
• To extend the model for incomplete data using a pattern mixture approach.

Main Methods:

• Development of a joint quantile regression model incorporating both time-varying and time-constant random coefficients.
• Extension of the model to handle missing data via a pattern mixture framework.
• Validation through extensive simulation studies and application to real-world HIV CD4 count data.

Main Results:

• The proposed model effectively captures complex longitudinal data structures, including temporal shocks and individual heterogeneity.
• Simulation studies confirm the model's robust performance under various scenarios.
• The analysis of CD4 count data demonstrates the practical utility of the new methodology.

Conclusions:

• The developed quantile regression framework provides a powerful tool for analyzing longitudinal data with unobserved heterogeneity and temporal dynamics.
• The pattern mixture extension addresses data incompleteness, offering more reliable inferences.
• This approach enhances understanding of disease progression and other longitudinal processes.