Regression Models for Manifold-Valued Data from Longitudinal Studies

• Activity Number: 243
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Emil Cornea*+ and Hongtu Zhu and Joseph Ibrahim
• Companies: University of North Carolina at Chapel Hill and University of North Carolina at Chapel Hill and University of North Carolina
• Keywords: attention deficit hyperactivity disorder ; diffusion tensor ; manifold-valued longitudinal data ; planar shape ; random effect models ; planar shape

Abstract

The aim of the paper is to present a general regression framework for the analysis of manifold-valued data from longitudinal studies. We develop intrinsic random effect and semi-parametric regression models for analyzing manifold longitudinal data. We focus on symmetric positive definite (SPD) matrices and landmark-based planar shapes rising from manifold-valued imaging data to illustrate our methodological development. We present an intrinsic random effect model for SPD matrices in order to analyze the whole diffusion tensor across regions of interest, in multiple voxels along the fiber tracts, with clinical and behavioral variables from longitudinal studies, based on diffusion tensor imaging. We apply our semi-parametric models to the shape analysis of the corpus callosum from longitudinal studies and investigate whether the corpus callosum shape information is a potential biomarker for the diagnosis of attention deficit hyperactivity disorder.