Innovations in Bayesian Latent Structure Modeling with Biomedical Applications

Abstract

Advances in medical technology and data-collection methods have led to an explosion in complicated biomedical data sets over the past few decades. As scientists' ability to measure more and more variables grows, so do the challenges in subsequent statistical analysis. Data are often high-dimensional, with high correlations both among related variables and over space and time. As a result, public health questions that are simple to ask can sometimes be quite difficult to answer with data. To address some of these challenges, this dissertation develops several novel Bayesian modeling approaches to generate interpretable scientific insights. Throughout, these approaches infer and make use of low-dimensional latent structure in complex data to facilitate inferences in challenging settings. In Chapter 2, we propose a low-rank longitudinal factor regression (LowFR) model for determining the associations between a longitudinally measured mixture of chemical exposures and a subsequent health outcome. LowFR handles high correlations over both related chemicals and repeated measurements by flexibly reducing dimensionality through a novel factor regression approach. After motivating and describing the model, we apply it to analyzing data from the ELEMENT study, finding that diethyl and dibutyl phthalate metabolite levels in trimesters 1 and 2 of pregnancy are associated with altered glucose metabolism in adolescence. In Chapter 3, we develop a Bayesian hierarchical model for better understanding severity of obstructive sleep apnea (OSA) by quantifying patient heterogeneity in sleep stage dynamics, rates of OSA events, and critically, in the effect of a patient's OSA events on their subsequent sleep dynamics. Our model produces a vector of interpretable patient-level random effects, which can be summarized and related to clinical outcomes. We develop a novel approach for estimating Bayes-optimal clusters of patients based on these random effects, and show an association of these clusters with cognitive performance in the APPLES study that is missed by simpler analysis approaches. In Chapter 4, we propose a targeted empirical Bayes approach for modified estimation of joint latent factor models when the ultimate goal is regression. We show that estimating the residual variance in the response model separately from the rest of the parameters can lead to substantial improvements in predictive performance. In each chapter, we demonstrate the advantages of our approach over competitors through both simulations and analysis of real public health data.