In chapter one a Liability Threshold Mixed Linear Model (LTMLM) association statistic is introduced for ascertained case-control studies that increases power vs. existing mixed model methods for diseases with low prevalence, ...

Chapter 1: Since the early 2000s, evidence has accumulated for a significant differential effect of first-line antiretroviral therapy (ART) regimens on human immunodeficiency virus (HIV) treatment outcomes, such as CD4 ...

In this dissertation, we consider semi-parametric estimation problems under semi-supervised (SS) settings, wherein the available data consists of a small or moderate sized labeled data (L), and a much larger unlabeled data ...

One major aim of statistics is to systematically study outcomes of interest in a population by observing the properties of a sample of that population. Some outcomes, such as the total number of people infected in an ...

Case-control genetic sequencing studies are increasingly being conducted to identify rare variants associated with complex diseases. Oftentimes, these studies collect a variety of secondary traits--quantitative and qualitative ...

High-dimensional count data arising from multinomial sampling is ubiquitous in microbiome studies. This dissertation aims to develop flexible Bayesian framework to model high-dimensional count data, which provides reliable ...

In many empirical disciplines, scientific discovery is modularized into discrete papers each investigating one or more hypotheses. Synthesizing these modules of evidence is critical to inform a balanced and appropriately ...

Robust statistics have emerged as a family of theories and techniques for estimating parameters of a model while dealing with deviations from idealized assumptions. Examples of deviations include misspecification of ...

The explosion of data arising from advances in high throughput sequencing has allowed scientists to study genomics in far greater detail. However, this high resolution picture of cells often makes it difficult to see the ...

This dissertation work is motivated by two time-to-event data examples, where current statistical methods are inadequate in addressing the nuances of data and the corresponding scientific question(s) of interest. In Chapter ...