An Approach to Nonparametric Bayesian Analysis for High Dimensional Longitudinal Data Sets

Abstract

The goal of this thesis is to develop a more powerful and flexible nonparametric method for the analysis of longitudinal data arising from high throughput biological assays, such as arise in next generation sequence analysis, proteomics and metabolomics, by expanding on an existing approach. The method compared 2 groups by testing for differences in the time to upcrossings and downcrossings for all possible levels using standard nonparametric statistical methods for testing for differences between event times that are subject to censoring. The main problem with nonparametric approaches is their lack of power relative to parametric alternatives, hence methods that aim to redress the shortcomings of nonparametric methods would provide researchers with an approach that greatly enhances their ability to analyze data sets that have a potential impact on human health. Hence in this thesis, we first develop a Bayesian counterpart to rank based tests using the Dirichlet process mixture (DPM) prior. Then we expand this approach to tie sets of distinct level crossing problems together via a hierarchical model to develop a more powerful test. While focusing on the first passage time is useful, such an approach ignores data beyond the first passage time. Hence, we also explore the analysis of recurrent event data from a Bayesian semi-parametric perspective and examine under what conditions the consideration of recurrent events leads to a more powerful procedure. There are not universally agreed upon methods for nonparametric longitudinal analysis, especially in a high dimensional context. As such the thesis research could help fill this gap in the field.