Bayesian Nonparametric Models for Biomedical Data Analysis

TL;DR

This dissertation introduces novel nonparametric Bayesian models for biomedical data, focusing on tumor heterogeneity, phylogenetic relationships, and missing data, with validation through simulations and real datasets.

Contribution

It develops new Bayesian models that incorporate dependency structures and auxiliary information, advancing analysis of complex biomedical data.

Findings

Improved tumor subclone reconstruction using mutation pairs

Bayesian treed model captures dependencies among features

Effective handling of non-ignorable missing data with auxiliary info

Abstract

In this dissertation, we develop nonparametric Bayesian models for biomedical data analysis. In particular, we focus on inference for tumor heterogeneity and inference for missing data. First, we present a Bayesian feature allocation model for tumor subclone reconstruction using mutation pairs. The key innovation lies in the use of short reads mapped to pairs of proximal single nucleotide variants (SNVs). In contrast, most existing methods use only marginal reads for unpaired SNVs. In the same context of using mutation pairs, in order to recover the phylogenetic relationship of subclones, we then develop a Bayesian treed feature allocation model. In contrast to commonly used feature allocation models, we allow the latent features to be dependent, using a tree structure to introduce dependence. Finally, we propose a nonparametric Bayesian approach to monotone missing data in longitudinal studies with non-ignorable missingness. In contrast to most existing methods, our method allows for incorporating information from auxiliary covariates and is able to capture complex structures among the response, missingness and auxiliary covariates. Our models are validated through simulation studies and are applied to real-world biomedical datasets.