Analyzing wearable device data using marked point processes

This paper introduces two sets of measures as exploratory tools to study physical activity patterns: active-to-sedentary/sedentary-to-active rate function (ASRF/SARF) and active/sedentary rate function (ARF/SRF). These two sets of measures are complementary to each other and can be effectively used together to understand physical activity patterns. The specific features are illustrated by an analysis of wearable device data from National Health and Nutrition Examination Survey (NHANES). A two-level semiparametric regression model for ARF and the associated activity magnitude is developed under a unified framework using the marked point process formulation. The inactive and active states measured by accelerometers are treated as a 0-1 point process, and the activity magnitude measured at each active state is defined as a marked variable. The commonly encountered missing data problem due to device nonwear is referred to as "window censoring," which is handled by a proper estimation approach that adopts techniques from recurrent event data. Large sample properties of the estimator and comparison between two regression models as measurement frequency increases are studied. Simulation and NHANES data analysis results are presented. The statistical inference and analysis results suggest that ASRF/SARF and ARF/SRF provide useful analytical tools to practitioners for future research on wearable device data.