An upper bound to the benefits of implementing positive assortative matching in pooled testing

Dorfman pooled testing combines individual specimens (e.g., blood samples) into one test; if the pooled sample tests positive for infection, each specimen is tested separately. Under small prevalence levels, this method is known to reduce the expected number of tests required to screen a population, as individual tests only occur when a pooled test detects an infection. When conducting Dorfman testing, studies often recommend implementing positive assortative matching, i.e., pooling together samples with a similar risk 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 easy-to-compute upper bounds to the benefits of implementing Dorfman testing with positive assortative matching instead of matching samples randomly. Testers can then compare these upper bounds with the costs of estimating the probabilities of infection from each sample and then matching together those with similar risk of infection, to aid their decision on whether or not to implement this method.