Chronic diseases are the leading cause of death in the United States. Early detection of diseases like cancer can extend life and improve quality of life as well as reduce cost to health systems, freeing resources for other purposes. Recent discoveries of many new biomarkers are helping physicians identify early signs of chronic diseases, such as cancer. At the same time, these advances have made clinical decision making difficult because the available tests are not 100 percent reliable and sometimes cause false positive or false negative results. False positives lead to anxiety and unnecessary referral of patients for expensive and invasive tests, such as biopsies and radiological imaging; false negatives cause a disease to go undetected and potentially progress to a life threatening stage. Since no single biomarker on its own is considered satisfactory, attention is turning to ways to combine biomarkers into composite tests with better predictive characteristics. This project will develop mathematical models for investigating which tests to use, when to use them, and how to combine them to screen for diseases in a way that balances the benefits of early detection with the harms of false negative test results. The aim of this project is to create stochastic programming models and partially observable Markov decision processes that integrate screening, diagnosis, and treatment decisions over the complete lifecycle of a chronic disease to optimize population screening. New data-driven models will be created for optimal design of (a) one-time composite screening tests; (b) personalized dynamic protocols for screening over a patient's lifetime to optimally balance the competing goals of early disease detection and minimal cost and harm from screening. These problems are challenging because of their stochastic and combinatorial nature, the partially observable nature of early stage chronic diseases, and the fact that there are multiple stakeholders (patients, physicians, insurers) and therefore multiple criteria. Theoretical properties that provide insight into optimal screening strategies will be analyzed and used to design efficient algorithms and approximation methods for solving these problems using a combination of stochastic optimization and machine learning. The discoveries from this project will be used to investigate the optimal design of screening strategies that weigh the benefits of early detection with the potential harms of screening. Finally, these models will be used to determine ideal characteristics of new biomarkers that make them worthy of costly clinical investigation.