Pooled Testing: Determining The Optimum Pool Size To Minimize The Total Number Of Tests

In light of the rapidly spreading COVID-19 virus, the FDA has suggested pooling of samples in order to reduce the cost of testing a large population. Under this approach, several samples are pooled, and the pooled samples are first tested. If the pool tests negative, then the lab would have successfully tested many samples while consuming only the resources needed for a single test. If the pooled sample tests positive, then each sample that comprised the pool is individually tested. In this context, an important question for people in the field is “Given a certain overall infection rate among the population, what is the optimum pool size so that we can minimize the overall number of tests for a given number of individual samples?” In this paper, we derive this number both empirically and analytically. We also address the related question “Given a certain pool size, what is the maximum infection rate for which we can still gain in terms of the number of tests?”