Title: Analysis Approaches for Wearable Device Data
Description: Wearable devices, which track a subject’s activity (e.g. steps, calories, intensity) over time, have become a popular option for research studies which seek to better understand an individual’s physical activity in the day-to-day setting. This thesis looks to address three common problems within the wearable device setting; how to address missing data and incomplete wear time, what to do when large outlying values are present, and how many observation days are required to reasonably estimate various activity metrics of interest. Given the dense nature of observations from such devices, functional data analysis (FDA) provides a natural framework for analysis, and we seek to address the first problem related to missing data by leveraging generalized functional principal components analysis (GFPCA). In addressing the second problem related to outlying values, we leverage both FDA and the novel principal component pursuit (PCP) approach, which has seen limited application within the field, to separate on observed functional value into low-rank, sparse, and error component functions.

Finally, using a rich longitudinal data set, we provide insight into the third problem regarding what is an appropriate study length, utilizing the framework of measurement reliability which has been often applied in the activity data setting. Our results suggest that leveraging FDA methods can provide more accurate estimates of activity during periods of nonwear then current approaches, and that in the presence of large outliers more robust estimates of underlying activity and outlier presence can be determined by combining FDA methods and those of PCP. Finally, within our longitudinal cohort we show that current guidelines regarding the number of days necessary to achieve a reasonable measurement reliability are inaccurate, and often underestimate the true number of days required.