A Riemann Manifold Model Framework for Longitudinal Changes in Physical Activity Patterns

Physical activity (PA) is significantly associated with many health outcomes. The wide usage of wearable accelerometer-based activity trackers in recent years has provided a unique opportunity for in-depth research on PA and its relations with health outcomes and interventions. Past analysis of activity tracker data relies heavily on aggregating minute-level PA records into day-level summary statistics, in which important information of PA temporal/diurnal patterns is lost. In this paper we propose a novel functional data analysis approach based on Riemann manifolds for modeling PA and its longitudinal changes. We model smoothed minute-level PA of a day as one-dimensional Riemann manifolds and longitudinal changes in PA in different visits as deformations between manifolds. The variability in changes of PA among a cohort of subjects is characterized via variability in the deformation. Functional principal component analysis is further adopted to model the deformations and PC scores are used as a proxy in modeling the relation between changes in PA and health outcomes and/or interventions. We conduct comprehensive analyses on data from two clinical trials: Reach for Health (RfH) and Metabolism, Exercise and Nutrition at UCSD (MENU), focusing on the effect of interventions on longitudinal changes in PA patterns and how different modes of changes in PA influence weight loss, respectively. The proposed approach reveals unique modes of changes including overall enhanced PA, boosted morning PA, and shifts of active hours specific to each study cohort. The results bring new insights into the study of longitudinal changes in PA and health and have the potential to facilitate designing of effective health interventions and guidelines.