| Large amounts of gene expression data available in the public realm, provide us with the opportunity to study associations between genes. The Pearson product moment correlation is the most widely used measure to quantify associations between random variables. In this thesis, we explore what can be gained by studying intergene correlations in genomic data sets. Specifically, we explore some of the unmarked territory in gene/gene association studies by exploiting graph theoretic concepts. Associations between genes can be studied on a pairwise basis as well as on a global scale. Both approaches have their own distinct advantages. Pairwise association studies have long ignored the importance of negative correlations. In the first part of this thesis, we construct a computationally efficient statistical tool to carry out a systematic study of negative correlations, and provide a novel view of the global pattern of negative pairwise correlations. In the second part of the thesis, we propose a novel approach to analyze gene/gene associations at a global scale. We propose measures to capture the degree to which certain genes modulate the associations between other sets of genes. Then we develop efficient procedures for estimating these quantities from genome-scale expression data with minimal bias. Working within the framework of graphical Gaussian models we provide an interpretation of these metrics in a graph-theoretic context and address the issue of inferring the topology of genetic regulatory networks on a coarse scale. |
