Statistical Methods for Structured Multilevel Functional Data: Estimation and Reliability

The thesis investigates a specific type of functional data with multilevel structures induced by complex experimental designs. Novel statistical methods based on principal component analysis that account for different layers of correlations in the data are introduced. A robust metric is proposed to evaluate the reproducibility of replicated functional and imaging studies. Shrinkage-based methods are extended to functional and imaging data with no or few replicates, and studies with low reliability. The proposed estimator is shown to correct for measurement error and improve prediction at the subject level by borrowing strength from the population average. Methods have been motivated by and applied to high-throughput physical activity measurements and several brain imaging studies based on different modalities including functional magnetic resonance imaging (fMRI), voxel-based morphometry, and diffusion tensor imaging (DTI). Fast algorithms are developed to expand the applicability of the methods proposed to ultra-high dimensional data. Readers: Brain Caffo (JHSPH Biostatistics) Peter Calabresi (Director, JHMI Division of Neuroimmunology) Ciprian Crainiceanu (advisor, JHSPH Biostatistics) Jennifer Schrack (JHSPH Epidemiology)

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