Stochastic methods in cancer research : applications to genomics and angiogenesis

In recent years, interactions between mathematicians and biomedical researchers have increased due to both the complexity of the biological/medical issues and the development of new technologies, producing “large” data rich of information. Biomathematics is applied in many areas, such as epidemiology, clinical trial design, neuroscience, disease modeling, genomics, proteomics, etc. Cancer is a multistep process where the accumulation of genomic lesions alters cell biology. The latter is under control of several pathways and, thus, cancer can origin via different mechanisms affecting different pathways. However, usually, more than one of these mechanisms needs to be damaged before a cell becomes cancerous. Due to the general complexity of this disease and the different type of tumors, the efforts of cancer research cover several research areas such as, for example, immunology, genetics, cell biology, angiogenesis. As a consequence, many biostatistical topics can be applied. The thesis is divided into two parts. In the former, two Bayesian regression methods for the analysis of two types of cancer genomic data are proposed. In the latter, the properties of two estimators of the intensity of a stationary fibre process are studied, which can be applied for the characterization of angiogenic and vascular processes.