Analyzing longitudinal data using general linear mixed models versus generalized estimating equations

Abstract

In this dissertation two techniques will be put forward for analyzing longitudinal data; general linear mixed models and generalized estimating equations. These methods provide an improvement over repeated measures ANOV A which was traditionally used for analyzing longitudinal datasets. Both general linear mixed models and generalized estimating equations may in fact be used when repeated measurements, for the subjects/objects being considered, are taken at different time points, when missing data is present in the data and also when there is time dependent correlation between the repeated measurements. In the mixed models approach, the variance-covariance matrix for the repeated observations is a combination of two sources of variability; the within-subject variability and the between-subject variability. Due to the inclusion of what are known as random effects, the population parameters in such models are allowed to vary from one subject to the other and in this manner, subject-specific results could be obtained. Whilst linear mixed models are however only used with normally distributed data, GEE is based on the specification of the first two moments of a response variable, with the mean being related to the explanatory variables through the specification of a link function, and the correlation between the repeated measurements is accounted for through the specification of a working correlation structure. In adopting the latter approach, population-averaged results are obtained, contrasting them with the subject specific results obtained from the mixed models. The aim of this dissertation is to highlight the main characteristics of the two different approaches to model longitudinal data, both theoretically and also by using a real dataset. Results obtained on an Autism dataset will be compared and contrasted under the two approaches.