Breast cancer, the leading cause of cancer death for women, can be detected at earlier stages through screening. Therefore, several countries have implemented population-based mammography screening programs. While mammography is the gold standard for breast cancer screening, it has several drawbacks such as high rates of false positives that lead to patient anxiety and additional costs. Besides, most of the existing screening guidelines ignore individual risk factors for breast cancer, which may result in less frequent screening for high-risk women and unnecessary screenings for low-risk women. Therefore, careful design of breast cancer screening is crucial to minimize the potential harms of the screening and improving the health outcomes.

In this dissertation, we study three aspects of the breast cancer screening problem:​ impact of breast density and supplemental screenings, breast cancer screening in resource-restricted settings and racial disparities in breast cancer outcomes. We first analyze the impacts of breast density and supplemental tests on breast cancer screening policies. We formulate the optimal breast cancer screening problem using a discrete-time partially observable Markov decision process (POMDP) model. The state space of our model is composed of the patient’s health states and the breast density states. At each decision epoch, the physician first decides whether or not the patient should undergo mammography screening, and then uses the observed mammography result to decide whether or not to follow up with supplemental screening. Our numerical study demonstrates that incorporating breast density into the design of breast cancer screening policies can significantly affect the screening recommendations. In addition, we find that incremental benefit of supplemental tests over digital mammography is rather limited;​ in particular, patients with higher risk of breast cancer should be recommended more frequent mammography screenings instead of supplemental tests.

Next, we investigate the optimal allocation of limited mammography resources to screen a population. We propose a constrained POMDP model that maximizes total expected qualityadjusted life years of the patients when they are allowed only a limited number of mammography screenings. We use a variable resolution grid-based approximation scheme to convert the constrained POMDP model into a mixed-integer linear program and conduct several numerical experiments using breast cancer epidemiology data. We observe that as mammography screening capacity decreases, patients in the 40-49 age group should be given the least priority with respect to screening. We further find that efficient allocation of available resources between patients with different risk levels leads to significant quality-adjusted life year gains, especially for the patients with higher breast cancer risk.

Finally, we consider race as a risk factor for breast cancer and investigate the contributing factors leading to higher breast cancer mortality among black women. We modify the University of Wisconsin Breast Cancer Simulation model to obtain race-specific models and analyze the differences in disease natural history, treatment utilization and mammography uptake. Our findings indicate that targeted prevention and detection strategies that go beyond equalizing access to mammography may be needed to eliminate racial disparities.