An optimization framework for large-scale screening under limited testing capacity with application to COVID-19

We consider the problem of targeted mass screening of heterogeneous populations under limited testing capacity. Mass screening is an essential tool that arises in various settings, e.g., ensuring a safe supply of blood, reducing prevalence of sexually transmitted diseases, and mitigating the spread of infectious disease outbreaks. The goal of mass screening is to classify whole population groups as positive or negative for an infectious disease as efficiently and accurately as possible. Under limited testing capacity, it is not possible to screen the entire population and hence administrators must reserve testing and target those among the population that are most in need or most susceptible. This paper addresses this decision problem by taking advantage of accessible population-level risk information to identify the optimal set of sub-populations to target for screening. We conduct a comprehensive analysis that considers the two most commonly adopted schemes: Individual testing and Dorfman group testing. For both schemes, we formulate an optimization model that aims to minimize the number of misclassifications under a testing capacity constraint. By analyzing the formulations, we establish key structural properties which we use to construct efficient and accurate solution techniques. We conduct a case study on COVID-19 in the United States using geographic-based data. Our results reveal that the considered proactive targeted schemes outperform commonly adopted practices by substantially reducing misclassifications. Our case study provides important managerial insights with regards to optimal allocation of tests, testing designs, and protocols that dictate the optimality of schemes. Such insights can inform policy-makers with tailored and implementable data-driven recommendations.