The microbiome is inherently dynamic, driven by interactions among microbes, with the host, and with the environment. At any point in life, human microbiome can be dramatically altered, either transiently or long term, by diseases, medical interventions or even daily routines. Since the human microbiome is highly dynamic and personalized, longitudinal microbiome studies that sample human-associated microbial communities repeatedly over time provide valuable information for researchers to observe both inter- and intra-individual variability, or to measure changes in response to an intervention in real time. Despite this increasing need in longitudinal data analysis, statistical methods for analyzing sparse longitudinal microbiome data and longitudinal multi-omics data still lag behind. In this dissertation, we describe our efforts in developing two novel statistical methods, Bayesian functional principal components analysis (SFPCA) for sparse longitudinal data analysis, and multivariate sparse functional principal components analysis (mSFPCA) for longitudinal microbiome multi-omics data analysis.
Beyond longitudinal data analysis, we are also interested in utilizing statistical techniques for addressing the “reproducibility crisis” in microbiome research, especially in the indispensable task of feature selection. Instead of developing “the best” feature selection method, we focus on discovering a reproducible criterion called Stability for evaluating feature selection methods in order to yield reproducible results in microbiome analysis.
To set an appropriate motivation and context for our work, Chapter 1 reviews the importance of longitudinal studies in human microbiome research, and presents the crucial need of developing novel statistical methods to meet the new challenges in longitudinal microbiome data analysis, and of producing reproducible results in microbiome feature selection. Chapter 2 introduces Bayesian SFPCA, a flexible Bayesian approach to SFPCA that enables efficient model selection and graphical model diagnostics for valid longitudinal microbiome applications. Chapter 3 presents mSFPCA, an extension of Bayesian SFPCA from modeling a univariate temporal outcome to simultaneously characterizing multiple temporal measurements, and inferring their temporal associations based on mutual information estimation. Chapter 4 proposes to use reproducibility criterion such as Stability instead of popular model prediction metric such as mean squared error (MSE) to quantify the reproducibility of identified microbial features.