All ETDs from UAB

Advisory Committee Chair

Inmaculada B Aban

Advisory Committee Members

Charles R Katholi

Jeffery M Szychowski

Louis J Dell'Italia

Himanshu Gupta

Thomas S Denney

Document Type

Dissertation

Date of Award

2013

Degree Name by School

Doctor of Philosophy (PhD) School of Public Health

Abstract

The goal of this dissertation is to investigate applying currently available Frequentist spatial analysis methods to cardiovascular MRI (cMRI) data. This data is typically analyzed using methods dependent summary statistics; our goal is to analyze using the full dataset. In our first paper, we explore application of spatial covariance structures to cMRI data via a generalized linear model. In our second paper, we examine the effects of misspecification of the covariance structure when analyzing spatially correlated data utilizing generalized linear models via Monte Carlo simulation. Finally, in our third paper, we propose an alternative family of covariance structures that lends itself to clustered data; in particular, this family of covariance structures allows researchers to define each piece of the covariance matrix as applicable to the data at hand. In our research, we see that when analyzing cMRI data, spatial covariance structures fit best when overlooking the unstructured covariance structure. In our simulation, we discover that specifying the unstructured covariance structure results in an unacceptably high type I error. This simulation study shows that when the data is spatially correlated, we are best served to specify a spatial covariance structure as the working covariance as evidenced by type I and power rates. Finally, as an alternative to already available covariance structures, we propose a flexible covariance structure for clustered data that allows researchers to hand pick the structure applied to each group for both the within-group and between-group covariances. We develop a program to implement this new structure and obtain model estimates and performed simulation studies to validate the program and investigate the finite sample properties of the estimators. We observe that both the regression and covariance parameters are unbiased and the type I error is approximately 5% for the sample sizes and scenarios considered. We conclude with two examples to demonstrate the flexibility of our proposed structure.

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