Models for Longitudinal Data: A Generalized Estimating Equation Approach

TLDR

Assuming Gaussian subject‑specific parameters yields simple relationships between population‑averaged and subject‑specific model parameters. This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject‑specific models that explicitly model heterogeneity in regression parameters, and population‑averaged models that focus on the aggregate response; a generalized estimating equation approach is used to fit both classes for discrete and continuous outcomes. The methods are illustrated with an analysis of data on mothers’ smoking and children’s respiratory disease.

Abstract

This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mother's smoking and children's respiratory disease.