Capturing the dilution effect of risk‐based grouping with application to COVID‐19 screening

We investigate the problem of screening a large population for an infectious disease (i.e., classifying subjects as positive or negative) using group testing while considering important test and population‐level characteristics. Group testing, in which multiple samples are pooled together into a master sample and tested simultaneously, has the potential to significantly expand screening efforts, and, owing to the COVID‐19 pandemic, the topic has seen a surge of interest recently. In this paper, we construct optimal group testing designs that consider a heterogeneous population (i.e., with subject‐specific risk), imperfect tests, and while also modeling the dilution effect of grouping (a phenomenon in which the test accuracy of the master sample is affected by the concentration of the virus in the pool), which is often ignored in the literature. We conduct an exhaustive analysis under both a general dilution function and a specific (yet still calibratable) form of the dilution function. Our analytical results of the resulting challenging optimization problems unveil key structural properties that hold in an optimal solution, which we utilize to construct efficient solution schemes. We complement the analysis with two case studies, one on the screening of blood for the Hepatitis B Virus and the other on the screening of subjects for COVID‐19. Our results reveal significant benefits over current practices, individual testing, as well as prior studies that ignore the dilution effect. Such results underscore the importance of incorporating both test and population‐level characteristics into the modeling framework.