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Principal Investigator  
Principal Investigator's Name: Shan Yu
Institution: University of Virginia
Department: Department of Statistics
Country:
Proposed Analysis: Motivated by recent work of analyzing data in the biomedical imaging studies, we develop a class of longitudinal spatially varying coefficient models and apply linear functional regression for imaging responses and scalar predictors. In this project, we will use the proposed model to study the spatially normalized Positron Emission Tomography (PET) data of Alzheimer's Disease Neuroimaging Initiative (ADNI) and understand the disease's progress. The finding of our results can be used for the early detection of Alzheimer's Disease. We propose to use flexible bivariate splines over triangulations to handle the irregular domain of the objects of interest on the images and other characteristics of images. The proposed spline estimators of the coefficient functions are proved to be root-$n$ consistent and asymptotically normal under some regularity conditions. Asymptotic confidence intervals and data-driven confidence corridors (CCs) for the coefficient functions are constructed, which can be served as trustful statistical inference tools. Our method can simultaneously estimate and make inferences of the coefficient functions while incorporating spatial heterogeneity and spatial correlation. A highly efficient and scalable estimation algorithm is developed to handle large biomedical imaging data.
Additional Investigators  
Investigator's Name: Hyunjae Cho
Proposed Analysis: The study is motivated by investigating longitudinal data analysis in brain image studies conducted at different phases. To explore the association between imaging responses and scalar predictors, we propose longitudinal image-on-scalar regression. To deal with the irregular domain of brain image, the study employed bivariate splines over triangulations. The proposed coefficient estimators are derived through the least square estimation with a penalty term using the energy function. To address the computational challenge, we suggest a parallel computing solution that uses the domain decomposition algorithm (DDC) and Hilbert filling curve for basis selection methods. The study's novelties lie in the division and conquer method, where the proposed longitudinal-image-on-scalar regression provides consistent and computationally efficient estimators while selecting uniformly distributed sample subregions. In addition, the proposed method can delineate the brain activity changes at different regions over different time points. We will use the ADNI dataset to conduct longitudinal brain imaging studies.