Defense Date


Document Type


Degree Name

Master of Science



First Advisor

Jessica Ketchum


Mixed-effects models are commonly used to model longitudinal data as they can appropriately account for within and between subject sources of variability. Univariate mixed effect modeling strategies are well developed for a single outcome (response) variable that may be continuous (e.g. Gaussian) or categorical (e.g. binary, Poisson) in nature. Only recently have extensions been discussed for jointly modeling multiple outcome variables measures longitudinally. Many diseases processes are a function of several factors that are correlated. For example, the metabolic syndrome, a constellation of cardiovascular risk factors associated with an increased risk of cardiovascular disease and type 2 diabetes, is often defined as having three of the following: elevated blood pressure, high waist circumference, elevated glucose, elevated triglycerides, and decreased HDL. Clearly these multiple measures within a subject are not independent. A model that could jointly model two or more of these risk factors and appropriately account for between subjects sources of variability as well as within subject sources of variability due to the longitudinal and multivariate nature of the data would be more useful than several univariate models. In fact, the univariate mixed-effects model can be extended in a relatively straightforward fashion to define a multivariate mixed-effects model for longitudinal data by appropriately defining the variance-covariance structure for the random-effects. Existing software such as the PROC MIXED in SAS can be used to fit the multivariate mixed-effects model. The Fels Longitudinal Study data were used to illustrate both univariate and multivariate mixed-effects modeling strategies. Specifically, jointly modeled longitudinal measures of systolic (SBP) and diastolic (DBP) blood pressure during childhood (ages two to eighteen) were compared between participants who were diagnosed with at least three of the metabolic syndrome risk factors in adulthood (ages thirty to fifty-five) and those who were never diagnosed with any risk factors. By identifying differences in risk factors, such as blood pressure, early in childhood between those who go on to develop the metabolic syndrome in adulthood and those who do not, earlier interventions could be used to prevent the development cardiovascular disease and type 2 diabetes. As demonstrated by these analyses, the multivariate model is able to not only answer the same questions addressed as the univariate model, it is also able to answer additional important questions about the association in the evolutions of the responses as well as the evolution of the associations. Furthermore, the additional information gained by incorporating information about the correlations between the responses was able to reduce the variability (standard errors) in both the fixed-effects estimates (e.g. differences in groups, effects of covariates) as well as the random-effects estimates (e.g. variability).


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VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

November 2009

Included in

Biostatistics Commons