Functional Data Analysis Methods for Analyzing Accelerometry Data in Mobile Health

Abstract

Accelerometry data collected by high-capacity sensors present a primary data type in smart mobile health. Such data enable scientists to extract personal digital features that are useful for precision health decision making. Existing methods in accelerometry data analysis typically begin with discretizing summary single-axis counts by certain fixed cutoffs into several activity categories; one well-known limitation is that the chosen cutoffs have often been validated under restricted settings, and thus they cannot be generalizable across populations, devices, or studies. Motivated by the Early Life Exposure in Mexico to ENvironmental Toxicants (ELEMENT) research cohort, in this dissertation I develop data-driven approaches to overcome this bottleneck in the analysis of physical activity (PA) data. In Chapter 2, I propose to holistically summarize an individual subject’s activity profile using Occupation Time curves (OTCs). Being a functional predictor, OTCs describe the percentage of time spent at or above a continuum of activity count levels. The resulting functional curve is informative to capture time-course individual variability of physical activities. I develop a multi-step adaptive learning algorithm, termed FRACT (Functional Regularized Adaptive Changepoint-detection Technique), to perform supervised learning via scalar-on-function regression modeling that involves OTC as the functional predictor as well as other scalar covariates. This learning analytic first incorporates a hybrid approach of fused lasso for clustering and Hidden Markov Model for change-point detection, and then executes a few refinement procedures to determine activity windows of interest. Through extensive simulation experiments I show the proposed FRACT performs well in both changepoint detection and regression coefficient estimation, and demonstrate its flexibility to determine data-driven associations based both on the underlying functional variables of interest, as well as the specific health outcomes, in a data analysis involving adolescent subjects from the ELEMENT cohort . In Chapter 3, I investigate functional analytics under an L0 regularization approach that enables the handling of highly correlated micro-activity windows that serve as predictors in the scalar-on-function regression model proposed in Chapter 2. Relatively recent advances in L0 regularization and discrete optimization have promoted this powerful optimization paradigm making it computationally viable. Utilizing such recent algorithmic and numeric capabilities, I develop a new one-step method that can simultaneously conduct fusion via change-point detection and parameter estimation through a new L0 constraint formulation. This new approach is not only computationally efficient but also avoids propagation of subjective errors incurred in a multi-stage analytic. I evaluate and illustrate the performance of the proposed learning analytics through simulation experiments and a reanalysis of the relationship between PA and biological aging. In Chapter 4, I extend the L0 regularization framework of Chapter 3 to a longitudinal functional framework with repeated wearable data to understand the influence of serially measured functional accelerometer data on longitudinal health outcomes. This extension invokes Quadratic Inference Functions (QIF), with an aim to detect PA intensity windows and assess their population-average effects on children health outcomes. I consider a population-average effects model, and develop a regularized QIF via mixed integer optimization to carry out longitudinal data analysis. In contrast to the previous chapters, which considered PA data during a seven-day period, with the repeated measurements taken approximately two years after the first, I focus on a longitudinal study of PA patterns from late-adolescence into early adulthood on sub-scapular skin thickness (SSST), a measure of body composition representing truncal fat distribution.