Mixed-effects state-space models for analysis of longitudinal dynamic systems.

Area of Science:

• Biomedical Engineering
• Computational Biology
• Biostatistics

Background:

• Biomedical systems are increasingly understood at a cellular level due to new biotechnologies.
• Dynamic biomedical systems can often be modeled using differential or difference equations, similar to engineering systems.

Purpose of the Study:

• To propose a class of mixed-effects state-space models for analyzing longitudinal biomedical dynamic systems.
• To adapt and investigate Bayesian and maximum likelihood methods for parameter estimation in these novel models.
• To illustrate the application of these models using HIV dynamics data.

Main Methods:

• Developed mixed-effects state-space models incorporating longitudinal data features.
• Modified Bayesian approach using Gibbs sampling for posterior distribution exploration.
• Developed a Monte Carlo EM algorithm with Gibbs sampling for the maximum likelihood method.
• Conducted simulation studies to compare the proposed estimation methods.

Main Results:

• The proposed mixed-effects state-space models effectively handle within-subject correlations and between-subject variations in longitudinal data.
• Both the Bayesian and maximum likelihood methods provide viable approaches for parameter estimation.
• The models were successfully applied to an AIDS clinical trial dataset.

Conclusions:

• The proposed mixed-effects state-space models offer a flexible framework for analyzing biomedical dynamic systems.
• The developed Bayesian and maximum likelihood methods are effective for parameter estimation.
• These methodologies have potential applications in diverse areas like cancer research and genetic regulatory networks.