Needles in a Haystack: How Pooling Can Control Error Rates in Noisy Tests

Arockia David Roy Kulandai, Marquette University
J. Stella, Xavier Institute of Engineering Mahim
John Rose, Xavier Institute of Engineering Mahim
Thomas Schwarz, Marquette University

Published as part of the proceedings of the conference 2021 IEEE International Conference on Communications Workshops (ICC Workshops), (June 2021). DOI. © 2021 Institute of Electrical and Electronic Engineers (IEEE). Used with permission.


Testing many individuals for a reasonably rare condition using imperfect, time consuming, and expensive tests can be facilitated by pooling. Pooling groups samples from different individuals that are then tested for the existence of a pathogen. An individual is diagnosed as a carrier if a threshold of the tests to which the individual contributed samples is positive. Our assumptions dictate a testing strategy that is not adaptive, with the exception of retesting positively diagnosed persons individually. Pooling is a standard proposal to stretch the supply of test kits. We show that it can also be used to control the false positive and false negative rate of tests, as long as errors are attributable to the lack of quality in the tests themselves and not to a lack of progression in the disease process where what is testable has still to develop. As the medical response to a new pandemic becomes more sophisticated, quality issues with tests will be less prevalent and our contribution will loose value. However, at the beginning of a new pandemic, wide-spread pooling with imperfect tests can prevent the disease from becoming a pandemic.