| Breast cancer is one of the most common forms of cancer in US women. It is believed that early detection by screening mammography can reduce breast cancer mortality. To understand the impact of early detection, we need to understand the behavior of the tumor and its metastasis as a function of time. We develop two models for the natural history of breast cancer. One is used to estimate the distribution of the tumor doubling time for tumors that were detected in metastatic stage by relating the size of the detected tumor and the breast cancer survival.; The second model can be used to explain the trends in mortality. This model relates the size of the tumor to its stage at the time of detection. This model can be used to measure the stage shift introduced by early detection programs. Stage shift implies a better breast cancer survival, which may lead to a reduction in breast cancer mortality.; In the last chapter we study a general nonlinear regression model with censoring. This model is a generalization of the estimation method used in the growth rate model. We propose an estimator derived from an estimating equation. We use the theory of empirical processes to obtain uniform limit theorems and prove the consistency and asymptotic normality of the estimator. |
