DiLernia, Andrew2021-09-242021-09-242021-06https://hdl.handle.net/11299/224533University of Minnesota Ph.D. dissertation. June 2021. Major: Biostatistics. Advisors: Lin Zhang, Mark Fiecas. 1 computer file (PDF); xii, 94 pages.Functional magnetic resonance imaging (fMRI) data is increasingly available and provides insight into the physiological mechanisms of the brain. As psychiatric disorders and many neurodegenerative diseases are intrinsically related to the brain, the availability of fMRI presents tremendous opportunities for improving understanding of these disorders and diseases. One approach for analyzing fMRI data is to describe functional connectivity (FC), the dependence of neuronal activity in regions of the brain. FC disruptions have been found in many mental disorders and diseases, so improving understanding of alterations in FC potentially underpinning mechanisms of these diseases is of clinical importance. Several metrics are used to describe FC connections such as marginal correlations, partial correlations, mutual information, and coherence among others. In this dissertation, we propose novel methods for inference and estimation of partial correlations for FC analysis of multi-subject fMRI data. In our first project, we consider heterogeneity of FC patterns and aim to cluster multi-subject fMRI data based on each individual's FC patterns. We propose a novel penalized model-based clustering method which simultaneously estimates FC and clusters subjects into groups with similar FC patterns. The method estimates the precision matrix, the elements of which give partial correlations of all pairs of variables, at both the subject and cluster level for bi-level FC inference. We apply the method to a multi-subject fMRI data set collected on participants diagnosed with schizophrenia and healthy controls finding that participants with schizophrenia were more likely to be clustered into a group with reduced FC connections. In our second project, we consider the issue of autocorrelation in fMRI data which is not accounted for in many existing methods when estimating and conducting inference of partial correlations. We derive an asymptotic joint distribution and novel covariance estimator for the partial correlations of a multivariate Gaussian process given mild regularity conditions. Based on the asymptotic distribution, we develop Wald confidence intervals and testing procedures for inference of individual partial correlations for inference of FC connections in single-subject fMRI data analysis. In our third project, we also use our theoretical result to propose a hierarchical model that directly accounts for the autocorrelation in fMRI data and within group heterogeneity. We then develop a novel testing procedure for two-group comparisons of group-level FC in terms of the partial correlations which is robust to various levels of autocorrelation present in fMRI data.enfMRIFunctional connectivityHierarchical modelPartial correlationSchizophreniaThesis or Dissertation