Author ORCID Identifier

Defense Date


Document Type


Degree Name

Doctor of Philosophy


Systems Modeling and Analysis

First Advisor

Edward L Boone


Past investigations utilizing Diffusion Tensor Imaging (DTI) have demonstrated that cocaine use disorder (CUD) yields white matter changes. We proposed three Bayesian techniques in order to explore the relationship between Fractional Anisotropy (FA), genetic data, and years of cocaine use (YCU). CUD participants exhibit abnormality in different areas of the brain versus non-drug using controls, which is measured by DTI. This dissertation is motivated by a neuroimaging genetic study in cocaine dependence, which found that there were relationships between several genes such as GAD and 5-HT2R and CUD subjects.

In the first chapter, there is background on the statistical methods that have been used to investigate the relationship between genetic factors and imaging features in the brain. Furthermore, chapter 1 discusses how the brain image was processed and how the genetic data was coded. Moreover, this chapter describes how individuals become participants in the study and what the criteria are for including or excluding an individual from the study. The rest of this chapter is devoted to literature reviews that support our presentation of the methodologies.

Chapter 2 explores the brain regions that indicate negative impact among interaction of GAD1a, GAD1b, and years of cocaine use by applying Bayesian model averaging with multiple linear regression. The novel contribution of this study is the demonstration of a series of two-way GAD1a | YCU , GAD1b | YCU and three-way GAD1a | GAD1b | YCU models which enable us to assess the individual contributions of each covariate in determining white matter changes in CUD.

Chapter 3 proposes more appropriate methods to analyze the data beyond linear regression. Since the response variable (FA) lies within the standard unit interval (0,1), linear regression has some limitations. In order to overcome this problem, we applied a Bayesian beta regression model. The underlying advantage of using the beta regression model is the flexibility that is achieved by the assumption that the response variable is following a beta distribution. Another advantage of this model is that it reparametrizes the beta parameters through link functions to get them in a linear form. The results suggest that the beta regression model is appropriate for use in imaging data with 3D information, and is also capable of analyzing an enormous number of datasets.

Chapter 4 extends Chapter 3 by accounting for spatial correlation. Our observations (voxels) are highly correlated due to their closeness to each other, without any gaps. Hence, we started by implementing the beta regression model, then extended the method by adding spatial correlation to all the regression coefficients, not only the mean. Due to the large number of voxels for the whole brain and the computation time, we applied the model to three regions of the brain (local estimate) instead of the entire brain (global estimate).

Many other methodologies, testing, and experiments have been left to be done in the future. In chapter 5, there are some ideas that have been proposed for future work. Some of them need a High Performance Computation cluster with large processors due to the high number of voxels.


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