Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Public Health

First Advisor

Ma, Shuangge

Abstract

Cancer is a molecular disease. In the past two decades, we have witnessed a surge of high- throughput profiling in cancer research and corresponding development of high-dimensional statistical techniques. In this dissertation, the focus is on gene expression, which has played a uniquely important role in cancer research. Compared to some other types of molecular measurements, for example DNA changes, gene expressions are “closer” to cancer outcomes. In addition, processed gene expression data have good statistical properties, in particular, continuity. In the “early” cancer gene expression data analysis, attention has been on marginal properties such as mean and variance. Genes function in a coordinated way. As such, techniques that take a system perspective have been developed to also take into account the interconnections among genes. Among such techniques, graphical models, with lucid biological interpretations and satisfactory statistical properties, have attracted special attention. Graphical model-based analysis can not only lead to a deeper understanding of genes’ properties but also serve as a basis for other analyses, for example, regression and clustering. Cancer molecular studies usually have limited sizes. In the graphical model- based analysis, the number of parameters to be estimated gets squared. Combined together, they lead to a serious lack of information.The overarching goal of this dissertation is to conduct more effective graphical model analysis for cancer gene expression studies. One literature review and three methodological projects have been conducted. The overall strategy is to borrow strength from additional information so as to assist gene expression graphical model estimation. In the first chapter, the literature review is conducted. The methods developed in Chapter 2 and Chapter 4 take advantage of information on regulators of gene expressions (such as methylation, copy number variation, microRNA, and others). As they belong to the vertical data integration framework, we first provide a review of such data integration for gene expression data in Chapter 1. Additional, graphical model-based analysis for gene expression data is reviewed. Research reported in this chapter has led to a paper published in Briefings in Bioinformat- ics. In Chapters 2-4, to accommodate the extreme complexity of information-borrowing for graphical models, three different approaches have been proposed. In Chapter 2, two graphical models, with a gene-expression-only one and a gene-expression-regulator one, are simultaneously considered. A biologically sensible hierarchy between the sparsity structures of these two networks is developed, which is the first of its kind. This hierarchy is then used to link the estimation of the two graphical models. This work has led to a paper published in Genetic Epidemiology. In Chapter 3, additional information is mined from published literature, for example, those deposited at PubMed. The consideration is that published studies have been based on many independent experiments and can contain valuable in- formation on genes’ interconnections. The challenge is to recognize that such information can be partial or even wrong. A two-step approach, consisting of information-guided and information-incorporated estimations, is developed. This work has led to a paper published in Biometrics. In Chapter 4, we slightly shift attention and examine the difference in graphs, which has important implications for understanding cancer development and progression. Our strategy is to link changes in gene expression graphs with those in regulator graphs, which means additional information for estimation. It is noted that to make individual chapters standing-alone, there can be minor overlapping in descriptions. All methodological developments in this research fit the advanced penalization paradigm, which has been popular for cancer gene expression and other molecular data analysis. This methodological coherence is highly desirable. For the methods described in Chapters 2- 4, we have developed new penalized estimations which have lucid interpretations and can directly lead to variable selection (and so sparse and interpretable graphs). We have also developed effective computational algorithms and R codes, which have been made publicly available at Dr. Shuangge Ma’s Github software repository. For the methods described in Chapters 2 and 3, statistical properties under ultrahigh dimensional settings and mild regularity conditions have been established, providing the proposed methods a uniquely strong ground. Statistical properties for the method developed in Chapter 4 are relatively straightforward and hence are omitted. For all the proposed methods, we have conducted extensive simulations, comparisons with the most relevant competitors, and data analysis. The practical advantage is fully established. Overall, this research has delivered a practically sensible information-incorporating strategy for improving graphical model-based analysis for cancer gene expression data, multiple highly competitive methods, R programs that can have broad utilization, and new findings for multiple cancer types.

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