After many years of biomedical research, biologists have accumulated much knowledge about genes' collaborative activity. This knowledge is summarized in the form of biological pathways. Knowledge about biological pathways turns out to be useful in genome research and many computational methods have been proposed to utilize this information in the analysis of high-dimensional data. However, many of these methods utilize pathway information in post hoc ways and pathways are hardly used in the modeling step. This dissertation studies statistical methods for systematically modeling gene dependency encoded in biological pathways. The first part of this dissertation models pathway group structure. Specifically, Chapter 2 develops a pathway-based gradient descent boosting procedure for nonparametric pathway-based regression (NPR) analysis of genomic data. Such NPR models treat genes in the same pathway as a group and consider multiple pathways simultaneously, while allowing complex interactions among genes within a pathway. Our simulation studies and real-world applications indicate that the NPR models can indeed identify relevant genes and pathways. The second part of this dissertation models pathway graphic structure and develops several Markov random fields (MRF) to model the dependency of gene expression patterns in biological pathways. Specifically, Chapter 3 proposes a hidden MRF (hMRF) model for analysis of non-temporal genomic data in microarray time course (MTC) data, genes exhibit not only pathway graphic dependency but also temporal dependency. Chapter 4 extends the hMRF model further into a hidden spatial-temporal MRF model to simultaneously consider the graphic and temporal dependencies for analysis of MTC data. Alternatively, for short MTC data with a few time points, Chapter 5 treats observed gene expression data as multivariate vectors and assume genes share the same expression patterns over time. A Bayesian framework with the hMRF model as the prior is employed. Different multivariate empirical Bayesian models are developed to serve as the emission probabilities for longitudinal and cross-sectional designs. Simulation studies and real-world applications, by utilizing pathway graphic structure information, show that these MRF-based models are quite effective in identifying genes and modified subnetworks with higher sensitivity than common procedures and comparable false discovery rates.
