Regularized Functional Regression Models with Applications to Brain Imaging.

[摘要] Positron emission tomography (PET) is an imaging technique that provides useful information about brain metabolism to help clinicians in the early diagnosis of Alzheimer;;s disease (AD). In order to identify the brain areas that show significant signals, many statistical methods have been developed for the analysis of brain imaging data. However, most of them neglect accounting for spatial information in imaging data. One way to address this problem is to treat each image as a realization of a functional predictor. This dissertation includes three research projects concerning regularized functional regression models via Haar wavelets for the analysis of brain imaging data, particularly PET images. The first project develops a lasso penalized 3D functional linear regression model by viewing PET image as a 3D functional predictor and cognitive impairment as the response variable, aiming to identify the most predictive voxels with the underlying assumption that only a few brain areas are truly predictive. The PET images are obtained from the Alzheimer;;s Disease Neuroimaging Initiative (ADNI) database. The second project concerns a lasso penalized 3D functional logistic regression model for classification of PET images from ADNI database. ADNI participants were classified into three groups during their initial visits: AD, Mild Cognitive Impairment (MCI) and Normal Control (NC). The model is applied to all the pairwise classifications using baseline PET images. The third project develops a regularized 3D multiple functional logistic regression model that can account for the group structure among voxels. Cerebral cortex can be partitioned into multiple regions. Treating each region as a group, within-group and groupwise regularization is imposed into the estimation to identify the most predictive voxels. This model is applied to the prediction of MCI-to-AD conversion using ADNI MCI subjects’ baseline PET images. All proposed models are evaluated through extensive simulation studies which are based on simulated data and slices extracted from ADNI PET images. Comparisons with existing methods for the prediction performance are also conducted using ADNI data. The results suggest that the proposed models are able to not only identify the predictive voxels, but also achieve higher prediction accuracy than existing methods in general.

[发布机构] University of Michigan

[效力级别] Alzheimer"

[关键词] Brain Imaging;Alzheimer"s Disease;Functional Regression;Haar Wavelets;Voxel Selection;PET;Statistics and Numeric Data;Science;Biostatistics