A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening

This paper presents a mathematical algorithm that computes the sizes and growth rates of breast cancer detected in a hypothetical population that is screened for the disease. The algorithm works by simulating the outcomes of the hypothetical population twice, first without screening and then with screening. The simulation without screening relies on an underlying model of the natural history of the disease. The simulation with screening uses this natural history model to track the growth of breast tumors backwards in the time starting from the time they would have been detected without screening. The method of tracking tumor growth backward in time is different from methods that track tumor growth forward in time by starting from an estimated time of tumor onset. The screening algorithm combines the natural history model, the method tracking of tumor growth backward in time, the age group, the interval between screening exams, and the detection threshold of the screening exam to compute the joint distribution of tumor size and growth rate among screen-detected and interval patients. The algorithm also computes the sensitivity and leadtime distribution. It allows for arbitrary age groups, detection thresholds and screening intervals and may contribute to the design of future screening trials.