Functional Data Analysis Methods for Wearable Device Data

Abstract

With the rapid development of sensor technologies, wearable devices have been increasingly used in engineering and health studies recently, which enable personalized assessment, intelligent monitoring, and early screening interventions. Wearable devices allow continuous monitoring of vital signs and biomedical signals, facilitating personal health tracking and evaluation. In recent decades, the advent of functional data analysis (FDA) methods provides opportunities to analyze sensor signals of personal fitness profiles and identify high-risk characteristics on health indicators in various regression models. The FDA of wearable device data collected in large cohort studies is challenging because (i) the interpretability of sophisticated functional linear model is difficult; (ii) the computational burden of estimation procedure is intensified when facing large-scale datasets, i.e. large sample size and high dimensional functional data; (iii) unified statistical inferential tools are little studied for generalized functional data. Therefore, we propose three novel FDA methods, comprising comprehensive modeling framework, estimation algorithm, and statistical inference.

First, we propose a new Functional Adaptive Double-Sparsity (FadDoS) estimator to improve the interpretability of a scalar-on-function regression model, where health outcomes are scalar responses and high-dimensional sensor signals serve as multiple functional covariates. Our estimator utilizes functional regularization of sparse group lasso with multiple functional predictors. This estimator achieves global sparsity through functional variable selection and local sparsity through zero-subinterval identification within coefficient functions. The FadDoS estimator is proven to converge at a bounded rate and satisfy the oracle property under mild conditions. The method is applied to a Kinect sensor study of the elderly in Hong Kong.

Second, motivated by Shanghai school adolescent accelerometry data structure, we propose an innovative two-dimensional functional mixed-effect model (2dFMM) for the repeatedly measured functional data, which smoothly varies over longitudinal day observations with covariate-dependent mean and covariance functions. The modeling framework characterizes the longitudinal and functional structures while incorporating two-dimensional fixed effects for covariates of interest. We also develop a fast three-stage estimation procedure to provide accurate fixed-effect inference for model interpretability and improve computational efficiency when encountering large datasets. We find strong evidence of intraday and interday varying significant associations between physical activity and mental health assessments among our cohort population, which shed light on possible intervention strategies targeting daily physical activity patterns to improve school adolescent mental health. Our method is also used in environmental data to illustrate its wide applicability.

Third, while prior work has focused on continuous responses in analyzing repeatedly measured functional data from dense longitudinal or spatial visits, discrete responses like binary curves are also important. Thus, we propose a two-dimensional generalized mixed-effect model (2dGFMM) to handle Gaussian or Dichotomous functional responses. The bivariate coefficient functions are estimated in a unified "pointwise-smoothing" pipeline with the help of various M-estimators. We further develop unified statistical inferential tools by subject-level bootstrap algorithm to test the two-dimensional varying effect. Extensive simulation studies compare the performance of non-robust and robust estimation and provide suggestions of choices under various measurement error conditions. The applications to physical activity data and weather data demonstrate the applicability of the proposed methods.

In the end, we summarize our contributions and discuss some future methods for wearable device data. Some possible research directions include the colinearity of multiple functional covariates and the nonlinearity of additive component functions for more general functional models.

Date of Award	14 Nov 2024
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Xinyue LI (Supervisor)