Integrating Machine Learning and Optimization Methods for Imaging of Patients with Prostate Cancer

We combine predictive modeling techniques from machine learning and optimization methods to design coordinated imaging protocols for detection of metastatic cancer. Our approach considers different combinations of imaging tests to reduce imaging while also ensuring that the average risk of missing a metastatic cancer in the population does not exceed a desirable threshold. To account for the imperfect calibration of probability estimates obtained from predictive models, we formulate the decision problem of determining the optimal assignment of patients to imaging protocols as a robust mixed-integer program. Furthermore, we propose fast, easy-to-understand and clinically motivated approximation algorithms that can mitigate the effects of statistical error in predictions. We illustrate the practical performance of the proposed approximation algorithms and optimization models based on medical data collected by a large state-wide prostate cancer collaborative. The work presented in this article will help lay the groundwork to improve medical decision making by integrating machine learning and optimization in other disease areas.