Diffusion-weighted magnetic resonance imaging (MRI) provides a unique approach to understand the geometric structure of brain fiber bundles and to delineate the diffusion properties across subjects and time. It can be used to identify structural connectivity abnormalities and helps to diagnose brain-related disorders. The aim of this paper is to develop a novel, robust, and efficient dimensional reduction and regression framework, called hierarchical functional principal regression model (HFPRM), to effectively correlate high-dimensional fiber bundle statistics with a set of predictors of interest, such as age, diagnosis status, and genetic markers. The three key novelties of HFPRM include the simultaneous analysis of a large number of fiber bundles, the disentanglement of global and individual latent factors that characterizes between-tract correlation patterns, and a bi-level analysis on the predictor effects. Simulations are conducted to evaluate the finite sample performance of HFPRM. We have also applied HFPRM to a genome-wide association study to explore important genetic variants in neonatal white matter development.
Keywords: Factor Analysis; Fiber Bundle Statistics; Functional Principal Component Analysis; Imaging Genetics; Varying Coefficient Model.