Methods for Functional Data Analysis of Wearable Device and Biomedical Imaging Data

In functional data analysis for longitudinal data, the observation process is typically assumed to be noninformative, which is often violated in real appli- cations. Thus, methods that fail to account for the dependence between observation times and longitudinal outcomes may result in biased estimation. For longitudinal data with informative observation times, we find that under a general class of shared random effect models, a commonly used functional data method may lead to inconsistent model estimation while another functional data method results in consistent and even rate-optimal estimation. Indeed, we show that the mean function can be estimated appropriately via penalized splines and that the covariance function can be estimated appropriately via penalized tensor-product splines, both with specific choices of parameters. For the proposed method, theoretical results are provided, and simulation studies and a real data analysis are conducted to demonstrate its performance. 

Self-reported measures of episodically consumed foods are often used in dietary assessments; however, they are prone to excess zeroes and measurement errors associated with periods of non-consumption and recall bias, respectively. Similarly, wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data prone to excess zeroes associated with periods of inactivity and with poorly characterized systematic errors. In this work, we propose semicontinuous modeling approaches for correcting biases due to measurement errors and missing data associated with functional and scalar covariates prone to excess zeroes and classical measurement error in sparse conditional functional quantile regression models. Our proposed semicontinuous models are composed of two parts, the first part is associated with periods of inactivity or non-wear and excess zeroes, while the second component is associated with the observed non-zero measures. We assume zero inflated exponential family models for the error prone device-based PA and self-reported dietary data and develop semicontinuous zero-inflated methods for bias corrections. 

In this talk, we will discuss Bayesian quantile functional regression methods for regressing distributional responses on predictors with possible smooth nonlinear covariate and longitudinally varying effects. We will apply this method to biomedical imaging data from multiple sclerosis and glioblastoma patients, and activity data from wearable devices. We will discuss our general modeling framework that accommodates any number of linear or nonlinear covariates, multiple levels of random effect functions, and spatial/temporal between function correlation, plus we will describe our sparse basis function representation, Bayesian inferential approaches, and introduce functional data analysis methods to adjust for potentially nonignorable missingness in the activity data example.