An Upper Bound to the Benefits of Implementing Positive Assortative Matching in Pooled Testing

Abstract

When conducting Dorfman testing, studies frequently recommend implementing positive assortative matching, i.e., pooling together samples with a similar likelihood of infection, as this tends to minimize the expected number of tests, the expected number of false negatives, and the expected number of false positives. However, because the logistics of collecting data and assorting samples from lowest to highest probability of infection can be costly, one may ask if implementing this procedure is indeed cost-effective. This article provides an easy-to-compute upper bound to the benefits of implementing Dorfman testing with positive assortative matching instead of matching samples randomly. Testers can then compare this upper bound with the costs of labeling and sorting samples from lowest to highest probability to aid their decision on whether or not to implement this method.

Keywords: Dorfman Screening, Random Matching, Ordered Pooling, Group Testing