Inverse optimization for assessing emerging technologies in breast cancer screening

Identifying the optimal screening strategies for breast cancer, the second leading cause of female cancer deaths in the US, is a major societal problem creating much controversy. The optimal screening strategies significantly depend on the sensitivity and specificity of the screening modality used. While the current state-of-the-art screening technology is mammography, its sensitivity or specificity may increase over time, or mammography may be replaced by another technology such as tomosynthesis in the near future. The purpose of this study is to identify the optimal use of the next generation of breast cancer screening modalities, whose sensitivity and specificity in clinical practice are either yet unknown or keep improving over time. Contrary to the prior literature that focuses on finding the optimal screening policy for given sensitivity and specificity values, we take an inverse optimization approach and focus on finding the range of sensitivity and specificity values, for which a given screening policy is optimal. To replicate breast cancer progression in the US population under various screening policies, we develop a parametric Partially Observable Markov Chain (POMC) model, which accounts for unobservable and age-specific disease progression, age-specific mortality, and the possibility of detecting cancer without a screening exam (either via self-detection or a clinical breast exam). We then formulate a nonlinear program (NLP) to identify the range of sensitivity and specificity values that optimize a particular screening policy. We show that this NLP is nonconvex for some parameter values, and hence difficult to solve. We prove several structural properties of the model, and by exploiting these properties, we propose a complete solution algorithm for this problem. We use real data in our numerical analysis and show that with the current technology, biennial breast cancer screening is slightly better than annual screening for the average-risk population. We also find that an improvement only in sensitivity (but not in specificity) will not change the current optimal policy. Furthermore, we characterize the lost potential quality-adjusted life years (QALYs) due to suboptimal practice, and show that biennial screening is more robust than annual screening in the sense that it results in fewer lost QALYs due to choosing a suboptimal screening policy. Given that the design of multicenter clinical trials may be prohibitively expensive and lengthy, our findings may be especially valuable to policymakers in deciding about the optimal use of an emerging breast cancer screening modality, and adapting a new technology in different settings. Copyright Springer Science+Business Media New York 2015