Conservative two-stage group testing in the linear regime

TL;DR

This paper analyzes conservative two-stage group testing in the linear regime, establishing near-optimal test designs and bounds, especially as prevalence approaches zero, with simulations supporting the theoretical findings.

Contribution

It introduces a new lower bound for tests in conservative two-stage group testing and identifies a near-optimal first-stage design for all prevalences.

Findings

First-stage design is nearly optimal across all prevalences.

The derived lower bound closely matches the performance of the studied design.

Simulations confirm the theoretical predictions.

Abstract

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.