  Inspired by applications in testing for Covid-19, we consider a variant of
two-stage group testing called "conservative" (or "trivial") 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
as studied by Broder and Kumar (arXiv:2004.01684) with constant tests per item
and constant items per test is extremely close to optimal for all prevalences,
and is optimal in the limit as the prevalence tends to zero. Simulations back
up the theoretical results.
