Conservative two-stage group testing

Inspired by applications in testing for COVID-19, we consider a variant of two-stage group testing we call "conservative" two-stage testing, where every item declared to be defective must be definitively confirmed by being tested by itself in the second stage. We study this in the linear regime where the prevalence is fixed while the number of items is large. We study various nonadaptive test designs for the first stage, and derive a new lower bound for the total number of tests required. We find that a first-stage design with constant tests per item and constant items per test due to Broder and Kumar (arXiv:2004.01684) is extremely close to optimal. Simulations back up the theoretical results.