Statistical Methods for Multilevel Multivariate Functional Studies

Abstract. Multiple Sclerosis (MS) is an immune-mediated disease of the central nervous system (CNS) that affects an estimated 400; 000 people in the United States alone. MS is characterized by focal demyelinating lesions and causes physical and cognitive impairment. While imaging stud- ies are widely used in clinical practice and research, the number of targeted and strongly predictive neuroimaging-based biomarkers is small. Thus, we focus on two promising imaging modalities that are likely to capture complementary information on MS disease severity and dynamics: (1) longitudinal changes in white matter integrity captured by Diffusion Tensor Imaging (DTI) across the corpus cal- losum; and (2) longitudinal changes in the voxel intensities of MS lesions in multi-sequence Magnetic Resonance Imaging (MRI). To address these emerging data structures we propose realistic biostatisti- cal methods that can scale up and produce principled inference for longitudinal high dimensional data. The first Aim is focused on massively univariate generalized linear mixed effects models (MU-GLMMs) and proposes a simple inferential approach for dealing with the within- and between-study participant correlation. The second Aim is concerned with the joint modeling of dense longitudinal high dimen- sional data (e.g., lesion voxel intensities) and survival time (e.g., time to voxel recovery). The third Aim is designed to quantify the association between the longitudinal neuroimaging and established MS biomarkers. The fourth Aim is dedicated to implementation, software, and reproducibility.