Fast Univariate Inference for Longitudinal Functional Models

• Activity Number: 62 - Large Population Physical Activity Studies Using Wearable Devices: Challenges and Future Directions
• Type: Invited
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Erjia Cui* and Andrew Leroux and Ciprian Crainiceanu and Ekaterina Smirnova
• Companies: Johns Hopkins Bloomberg School of Public Health and University of Colorado Anschutz Medical Campus and Johns Hopkins University and Virginia Commonwealth University
• Keywords: functional data; longitudinal data; accelerometry; DTI

Abstract

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (1) fit massively univariate pointwise mixed effects models; (2) apply any smoother along the functional domain; and (3) obtain joint con?dence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (1) Diffusion Tensor Imaging (DTI) measured at multiple visits along the corpus callosum of multiple sclerosis (MS) patients; and (2) physical activity data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the physical activity data application. Methods are accompanied by R software, though the method is “read-and-use”, as it can be implemented by any analyst who is familiar with mixed effects model software.