The Geometry of Cancer

Abstract

Cancer is a complex, multifaceted disease that operates through dynamic changes in the genome. Cancer is best understood through the process that generates it -- random mutations operated on by natural selection -- and several global hallmarks that describe its broad mechanisms. While many genes, protein interactions, and pathways have been enumerated as a kind of ``parts'' list for cancer, researchers are attempting to synthesize broader models for inferring and predicting cancer behavior using high-throughput data and integrative analyses. The focus of this thesis is on the development of two novel methods that are optimized for the analysis of complex cancer phenotypes. The first method incorporates ideas from gradient learning with multitask learning to assess statistical dependencies across multiple related data sets. The second method integrates multiscale analysis on graphs and manifolds developed in applied harmonic analysis with sparse factor models, a mainstay of applied statistics. This method generates multiscale factors that are used for inferring hierarchical associations within complex biological networks. The primary biological focus is the inference of gene and pathway dependencies associated with cancer progression and metastatic disease in prostate cancer. Significant findings include evidence of Skp2 degradation of the cell-cycle regulator p27, and the upstream deregulation of the TGF-beta pathway, driving prostate cancer recurrence.