Date of Award


Document Type

Open Access Dissertation


Epidemiology and Biostatistics

First Advisor

Hongmei Zhang


Functional neuroimaging is a relatively young discipline within the neurosciences that has led to significant advances in our understanding of the human brain and progress in neuroscientific research related to public health. Accurately identifying activated regions in the brain showing a strong association with an outcome of interest is crucial in terms of disease prediction and prevention. Functional magnetic resonance imaging (fMRI) is the most widely used method for this type of study as it has the ability to measure and identify the location of changes in tissue perfusion, blood oxygenation, and blood volume. In practice, the three-dimensional brain locations or coordinates of the local maximum of these changes are reported. By nature, fMRIs are noninvasive, slowly becoming more available, have relatively high spatiotemporal resolution, and have the remarkable ability to map the entire network of the brain’s function during the thought process. However, due to their high costs, fMRI studies tend to have a very small number of participants, which cause inflated type II error and lack reproducibility. This gives rise to the need for fMRI meta analyzes, which combines studies in order to increase overall sample size and testing power. In this dissertation, two methods are proposed that aim to identify regions of brain activation using fMRI coordinate-based meta analysis; a spatial Cox process and a mixture of Dirichlet processes model. The first method was motivated by the desire to identify significant regions of brain activation using fMRI coordinate-based meta data. To identify these regions we elected to implement a Bayesian spatial Cox process. We considered two levels of clustering, latent foci center and study activation center, utilizing the Dirichlet process (DP) built into a spatial Cox process used to model the distribution of foci. Commonly used spatial clustering methods model the random variation of the intensity governed by a process such that peaks in these processes would relate to areas of elevated aggregation in the events. However, methods of this type all assume three-dimensional normality, which is inappropriate for fMRI due to the nature of brain functioning and brain structure, and can possibly cause misclassification of foci and increase error in prediction and estimation. We relax this normality assumption and model intensity as a function of distance between the focus and the center of the cluster of foci using Gaussian kernels and the foci center will be identified by the use of a Dirichlet process. Simulation studies were conducted to evaluate the sensitivity and robustness with respect to cluster identification and underlying data distributions. An additional application of the proposed method was applied to an fMRI meta data of emotion foci. Both simulations and real data application produced promising results that highlighted the ability to correctly cluster. The second method was motivated by the spatial Cox process’ inability to statistically distinguish between clusters via a limitation to the Dirichlet process. However, it still aimed to identify significant regions of brain activation. This method modeled the realization of the data as a linear association with the overall mean of the data and adjusts for some study effect. The mean of the data was modeled as a mixture of unknown finite number of components and adjusted for a study effect modeled as a Dirichlet process. Similarly, each component was modeled as a Dirichlet process. Conditional on the mean of the data and some study effect, the distribution of the random error is standard multivariate normal. By modeling the mean as a mixture of Dirichlet processes, this still allows the method flexibility in capturing irregular spatial patterns and relaxes the typical normality assumptions, but can also statistically distinguish between a cluster or a mode within a cluster. The Bayesian framework was again implemented to draw model inferences. Simulation studies were

conducted to explore the sensitivity and robustness of the method, but illustrated a mediocre ability to correctly identify clusters. As an additional application, we applied the proposed method to the same fMRI meta data as was done in the first proposed method. The number of clusters identified were significantly lower and cluster centers identified were not in close proximity to any of those identified in the first proposed method. Both simulation studies and real data applications indicate this second proposed method is not sensitive enough to correctly identify clusters.