The goal of my thesis is to assess the impacts of cigarette smoking and genetic susceptibility on the onset lung cancer and to compute the age-specific probability of developing lung cancer given risk factor levels. The improvement in predicting the chance of having lung cancer at certain age will enhance physicians' capability to design a sensible screening strategy for early tumor detection in a high-risk population. This is the only way to reduce the mortality rate since no effective treatment or cure is available for advanced lung cancer at this time. The evaluation of the effects of these two risk factors proceeds through parameter estimation in the framework of the two-stage clonal expansion (TSCE) model applied to case-control study data. The TSCE model describes carcinogenesis as transitions from normal cells to slightly abnormal cells and to cancerous cells. Our data analysis indicates that smoking enhances the proliferation rate while both smoking and genetic susceptibility affect initiation and malignancy transformation rates. The data suggests that there might be a mechanism difference in the development of lung cancer for non-smokers and for smokers. Besides predicting survival rates, I rigorously prove the non-identifiability theorem for the TSCE model in the piecewise constant case and derive a new algorithm of calculating the survival function for a 3-stage and 2-path stochastic model. This 3-stage and 2-path model has two new features: it consists of two stages instead of one for abnormal cells, where one stage is more advanced than the other, and it includes two paths connecting normal cells to cancerous cells. The test of the new model on Texas cancer data shows a very good fit. Such efforts in developing models that incorporate new findings will lead to a better understanding of the mechanism of carcinogenesis and eventually to the development of drugs to treat cancer.