Mathematical modeling of pre-malignant lesions in multistage carcinogenesis

The etiology of cancer is largely unknown. However, considerable evidence supports the theory that multiple events are involved in carcinogenesis, the process of the transformation of normal cells into cancer cells.; The purpose of mathematical modeling in carcinogenesis is to improve our understanding of the biological processes involved in cancer formation and to provide a rational scientific basis for cancer risk assessment. In this dissertation, I develop mathematical formulations for the quantitative analysis of pre-malignant lesions within the framework of the multistage clonal expansion model: for example, Barrett's esophagus, a precursor (pre-malignant) lesion for esophageal adenocarcinoma; and adenomatous polyps, pre-malignant lesions for colorectal cancer.; I develop multistage carcinogenesis models that describe the age-specific incidence of adenocarcinoma of the esophagus and of the gastric cardia with separate adjustments for temporal trends due to birth cohort and period (calendar) effects. These models explicitly incorporate important features of pathogenesis of these cancers, such as the metaplastic conversion of normal esophagus to Barrett's esophagus.; Further, I develop mathematical expressions for the size distribution of screen-detectable pre-malignant lesions in tissue undergoing screening. I use these expressions to simulate the natural history of colorectal cancer and to evaluate the effect of a screen for adenomatous polyps and concomitant intervention on cancer risk. The approach used allows the efficient simulation of multiple screens and interventions. I demonstrate the utility of this approach by computing the optimal timing of screens and the benefits of up to two colonoscopies on the lifetime risk of colorectal cancer.