A bivariate autoregressive linear mixed effects model for the analysis of longitudinal data

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Clinical Research Methodology

Background:

• Dependent bivariate continuous responses in clinical studies often exhibit equilibrium over time.
• Modeling such longitudinal data requires methods that account for the interdependency and temporal dynamics of the variables.
• Existing univariate models may not fully capture the complexities of bivariate longitudinal data approaching equilibrium.

Purpose of the Study:

• To propose and illustrate an autoregressive linear mixed effects model for bivariate longitudinal data.
• To model the equilibrium of bivariate responses using fixed and random effects.
• To extend existing univariate longitudinal models to a bivariate context.

Main Methods:

• Developed an autoregressive linear mixed effects model where current bivariate responses are regressed on previous responses, fixed effects, and random effects.
• Incorporated fixed and random effects to model the equilibrium levels of the bivariate responses.
• Applied the model to analyze parathyroid hormone and serum calcium measurements in chronic hemodialysis patients.

Main Results:

• The proposed model effectively captures the dynamics of bivariate longitudinal data approaching equilibrium.
• The analysis of parathyroid hormone and serum calcium data demonstrates the practical application of the model in a clinical setting.
• The model provides insights into the factors influencing the equilibrium of these key biochemical markers.

Conclusions:

• The autoregressive linear mixed effects model is a valuable tool for analyzing bivariate longitudinal data with equilibrium.
• This approach enhances the understanding of complex biological systems and treatment effects in clinical studies.
• The model offers a robust framework for future research involving interdependent longitudinal measurements.