Microarray technology has flourished in the past decade and has been used extensively for functional genomic analysis. Tremendous research progress has been made in microarray data collection and analysis throughout this period. As microarray technology advances, subtle changes in the data are more common. Pathway analysis allows researchers to uncover biological meaningful sets of genes. It also has its advantages over widely used single gene-based analyses which are unable to take into account the dependencies between genes and are prone to multivariate testing issues. Several pathway-based methods have recently been proposed. However, these methods usually do not give consistent results, leaving room for the development of more efficient statistical methods and computational tools to better detect important pathways from microarray data. In this dissertation, we will first tackle the challenge of how to apply classification and regression methods to pathway-based analysis. Secondly, we will develop methods for clustering pathways and investigate possible interactions between them. The third project makes use of a random effects model for analyzing a pair of pathways. Lastly, we will propose a regularized shrinkage-based diagonal discriminant analysis for small sample size microarray data. Pathway-based tests for microarray data show great promise as a tool for biomedical research. Informative pathways may aid in the detection of disease at an early stage, help discover novel biomarkers and pinpoint target genes for possible interventions. Therefore, being able to identify important pathways associated with disease provides a new avenue for disease identification, prevention and diagnostics and has substantial public health impact.
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