Longitudinal Functional Principal Component Analysis with Application to DTI Tractography Data

• Activity Number: 502
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Sonja Greven*+ and Ciprian Crainiceanu and Brian Scott Caffo and Daniel Reich
• Companies: Ludwig-Maximilians-University Munich and The Johns Hopkins University and Johns Hopkins Bloomberg School of Public Health and National Institutes of Health
• Keywords: Diffusion tensor imaging ; Functional data analysis ; Karhunen-Loeve expansion ; Longitudinal data analysis ; Mixed effects model

Abstract

We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The model can be viewed as the functional analog of the classical mixed effects model where random effects are replaced by random processes. Methods have wide applicability. Computational feasibility for moderate and large data sets is assured by using principal component bases for the functional processes. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study designed to analyze differences and changes in brain connectivity in healthy volunteers and multiple sclerosis (MS) patients.