Group Testing Large Populations for SARS-CoV-2

Abstract

Group testing, the testing paradigm which combines multiple samples within a single test, was introduced in 1943 by Robert Dorfman. Since its original proposal for syphilis screening, group testing has been applied in domains such as fault identification in electrical and computer networks, machine learning, data mining, and cryptography. TheSARS-CoV-2 pandemic has led to proposals for using group testing in its original context of identifying infected individuals in a population with few tests. Studies suggest that non-adaptive group testing - in which all the tests are determined in advance - for SARS-CoV-2could help save 20% to 90% of tests depending on the prevalence. However, no systematic approach for comparing different non-adaptive group testing strategies currently exists. In this paper we develop a software platform for evaluating non-adaptive group testing strategies in both a noiseless setting and in the presence of realistic noise sources, modelled on published experimental observations, which makes them applicable to polymerase chain reaction (PCR) tests, the dominant type of tests for SARS-CoV-2. This modular platform can be used with a variety of group testing designs and decoding algorithms. We use it to evaluate the performance of near-doubly-regular designs and a decoding algorithm based on an integer linear programming formulation, both of which are known to be optimal in some regimes. We find savings between 40% and 91% of tests for prevalences up to 10% when a small error (below 5%) is allowed. We also find that the performance degrades gracefully with noise. We expect our modular, user-friendly, publicly available platform to facilitate empirical research into non-adaptive group testing for SARS-CoV-2.

Model-Based and Graph-Based Priors for Group Testing

“…In both the noiseless as noisy settings, the non-relaxed variant is an Integer Linear Program (ILP), whereas the relaxed version is a Linear Program (LP). There is numerical evidence that the LP solution is typically very close to the ILP solution in practice, while being cheaper to compute [2], [21], [22].…”

“…where ν takes the value that minimizes (22). It follows that for a fixed value of max{α * , β}, decreasing min{α * , β} does not affect the limit.…”

Tropical Group Testing

“…In this instance, the term quantitative refers to the fact that the tests' readings are non-binary and semi means that the readings are noisy or potentially inaccurate. Previous semiquantitative approaches are ill-suited for modeling the output of a PCR test as previous works mostly rely on the assumption that test measurements are reported on a linear (rather than a log) scale [Per20; DLO20; Aus20; Gho+21; She+20; YMX20; Yi+20; HN21; Coh+21; Pet+21; PBJ20; Lin+21 ;Zab+21] As an illustration of the potential problem of modeling the PCR test outputs on a linear scale, consider the Ct value of a test as the dB value of a sound wave or the pH value of a liquid. When adding a 50 dB white noise with a 30 dB one, we get a 50.04 dB white noise that is indistinguishable from 50 dB.…”