ADVANCED STATISTICAL LEARNING METHODS FOR HETEROGENEOUS MEDICAL IMAGING DATA

Most neuro-related diseases and disabling diseases display significant heterogeneity at the imaging and clinical scales. Characterizing such heterogeneity could transform our understanding of the etiology of these conditions and inspire new approaches to urgently needed preventions, diagnoses, and treatments. However, existing statistical methods face major challenges in delineating such heterogeneity at subject, group and study levels. In order to address these challenges, this work proposes several statistical learning methods for heterogeneous imaging data with different structures. First, we propose a dynamic spatial random effects model for longitudinal imaging dataset, which aims at characterizing both the imaging intensity progression and the temporal-spatial heterogeneity of diseased regions across subjects and time. The key components of proposed model include a spatial random effects model and a dynamic conditional random field model. The proposed model can effectively detect the dynamic diseased regions in each patient and present a dynamic statistical disease mapping within each subpopulation of interest. Second, to address the group level heterogeneity in non-Euclidean data, we develop a penalized model-based clustering framework to cluster high dimensional manifold data in symmetric spaces. Specifically, a mixture of geodesic factor analyzers is proposed with mixing proportions determined through a logistic model and Riemannian normal distribution in each component for data in symmetric spaces. Penalized likelihood approaches are used to realize variable selection procedures. We apply the proposed model to the ADNI hippocampal surface data, which shows excellent clustering performance and remarkably reveal meaningful clusters in the mixed population with controls and subjects with AD. Finally, to consider the potential heterogeneity caused by unobserved environmental, demographic and technical factors, we treat the imaging data as functional responses, and set up a surrogate variable analysis framework in functional linear models. A functional latent factor regression model is proposed. The confounding factors and the bias of local linear estimators caused by the confounding factors can be estimated and removed using singular value decomposition on residuals. We further develop a test for linear hypotheses of primary coefficient functions. Both simulation studies and ADNI hippocampal surface data analysis are conducted to show the performance of proposed method.Doctor of Philosoph