A tractable non-adaptative group testing method for non-binary measurements

TL;DR

This paper introduces a simple non-adaptive group testing algorithm that uses load measurements instead of binary responses, significantly reducing the number of tests needed to identify defective items, with applications in COVID-19 testing.

Contribution

It proposes a novel non-adaptive group testing method leveraging load measurements, improving efficiency over classical binary-response algorithms.

Findings

The method detects all defective items with fewer tests.

It is applicable to viral load testing in COVID-19 diagnostics.

The approach reduces testing resources under certain conditions.

Abstract

The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify all defective items of the collection with as few tests as possible. This problem is relevant in several fields, among which biology and computer sciences. In the present article we consider that the tests applied to groups of items returns a \emph{load}, measuring how defective the most defective item of the group is. In this setting, we propose a simple non-adaptative algorithm allowing the detection of all defective items of the collection. This method improves on classical group testing algorithms using only the binary response of the test. Group testing recently gained attraction as a potential tool to solve a shortage of COVID-19 test kits, in particular for RT-qPCR. These tests return the viral load of the sample and the viral load varies greatly among individuals. Therefore our model presents some of the key features of this problem. We aim at using the extra piece of information that represents the viral load to construct a one-stage pool testing algorithm on this idealized version. We show that under the right conditions, the total number of tests needed to detect contaminated samples can be drastically diminished.