Inference for the association between coefficients in a multivariate growth curve model

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Growth Curve Modeling

Background:

• Linear growth curve models are essential for analyzing longitudinal data.
• Understanding associations between individual-specific coefficients (e.g., slope and intercept) is crucial.
• Existing methods may not fully address complex associations in multi-variable, irregularly timed data.

Purpose of the Study:

• To generalize existing methods for inference on associations between growth curve coefficients.
• To develop and present statistical approaches for analyzing relationships between intercepts and slopes, or between slopes of different variables.
• To provide a framework for analyzing complex associations in longitudinal studies with irregular follow-up times.

Main Methods:

• Generalization of Blomqvist's work on linear growth curve models.
• Development of inference methods based on the method of moments.
• Development of inference methods based on maximum likelihood estimation.
• Asymptotic properties of the proposed inferential procedures are presented.

Main Results:

• The paper presents novel inferential approaches for analyzing associations between growth curve coefficients.
• Methodology is extended to accommodate polynomial growth curves and baseline covariates.
• The proposed methods are illustrated using a clinical trial dataset from a lung disease study.

Conclusions:

• The presented methodology offers advanced tools for statistical inference in linear growth curve models.
• The methods are applicable to longitudinal data with multiple response variables and irregular time points.
• The study provides a robust framework for investigating complex relationships between individual growth trajectories.