Consider a cohort of women, identified by year of birth, some of whom will eventually be diagnosed with breast cancer. A stochastic model is developed for predicting the U.S. breast cancer mortality that depends on advances in therapy and dissemination of mammographic screening. The predicted mortality can be compared with the same cohort having usual care with no screening program and absence of modern therapy, or a cohort in which only a proportion participate in a screening program and have modern therapy. The model envisions that a woman may be in four health states: i.e., 1) no disease or breast cancer that cannot be diagnosed (S0), 2) preclinical state (Sp), 3) clinical state (Sc), and 4) disease-specific death (Sd). The preclinical disease refers to breast cancer that is asymptomatic but that may be diagnosed with a special exam. The clinical state refers to symptomatic disease diagnosed under usual care. One of the basic assumptions of the model is that the disease is progressive; i.e., the transitions for the first three states are S0-->Sp-->Sc. The other basic assumption is that any reduction in mortality associated with earlier diagnosis is due to a stage shift in diagnosis; i.e., early diagnosis results in a larger proportion of earlier stage patients. The model is used to predict changes in female breast cancer mortality in the U.S. women for 1975-2000. The model is general and may predict mortality for other chronic diseases that satisfy the two basic assumptions.