A Recovery Algorithm and Pooling Designs for One-Stage Noisy Group Testing under the Probabilistic Framework

Group testing saves time and resources by testing each pre-assigned group instead of each individual, and one-stage group testing emerged as essential for cost-effectively controlling the current COVID-19 pandemic. Yet, the practical challenge of adjusting pooling designs based on infection rate has not been systematically addressed. In particular, there are both theoretical interests and practical motivation to analyze one-stage group testing at finite, practical problem sizes, rather than asymptotic ones, under noisy, rather than perfect tests, and when the number of positives is randomly distributed, rather than fixed.Here, we study noisy group testing under the probabilistic framework by modeling the infection vector as a random vector with Bernoulli entries. Our main contributions include a practical one-stage group testing protocol guided by maximizing pool entropy and a maximum-likelihood recovery algorithm under the probabilistic framework. Our findings high-light the implications of introducing randomness to the infection vectors – we find that the combinatorial structure of the pooling designs plays a less important role than the parameters such as pool size and redundancy.

Using viral load and epidemic dynamics to optimize pooled testing in resource-constrained settings

Virological testing is central to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) containment, but many settings face severe limitations on testing. Group testing offers a way to increase throughput by testing pools of combined samples; however, most proposed designs have not yet addressed key concerns over sensitivity loss and implementation feasibility. Here, we combined a mathematical model of epidemic spread and empirically derived viral kinetics for SARS-CoV-2 infections to identify pooling designs that are robust to changes in prevalence and to ratify sensitivity losses against the time course of individual infections. We show that prevalence can be accurately estimated across a broad range, from 0.02 to 20%, using only a few dozen pooled tests and using up to 400 times fewer tests than would be needed for individual identification. We then exhaustively evaluated the ability of different pooling designs to maximize the number of detected infections under various resource constraints, finding that simple pooling designs can identify up to 20 times as many true positives as individual testing with a given budget. Crucially, we confirmed that our theoretical results can be translated into practice using pooled human nasopharyngeal specimens by accurately estimating a 1% prevalence among 2304 samples using only 48 tests and through pooled sample identification in a panel of 960 samples. Our results show that accounting for variation in sampled viral loads provides a nuanced picture of how pooling affects sensitivity to detect infections. Using simple, practical group testing designs can vastly increase surveillance capabilities in resource-limited settings.

Construction of random pooling designs based on singular linear space over finite fields

<abstract><p>Faced with a large number of samples to be tested, if there are requiring to be tested one by one and complete in a short time, it is difficult to save time and save costs at the same time. The random pooling designs can deal with it to some degree. In this paper, a family of random pooling designs based on the singular linear spaces and related counting theorems are constructed. Furtherly, based on it we construct an $ \alpha $-$ almost\ d^e $-disjunct matrix and an $ \alpha $-$ almost\ (d, r, z] $-disjunct matrix, and all the parameters and properties of these random pooling designs are given. At last, by comparing to Li's construction, we find that our design is better under certain condition.</p></abstract>

Biological screens from linear codes: theory and tools

Molecular biology increasingly relies on large screens where enormous numbers of specimens are systematically assayed in the search for a particular, rare outcome. These screens include the systematic testing of small molecules for potential drugs and testing the association between genetic variation and a phenotype of interest. While these screens are ``hypothesis-free,'' they can be wasteful; pooling the specimens and then testing the pools is more efficient. We articulate in precise mathematical ways the type of structures useful in combinatorial pooling designs so as to eliminate waste, to provide light weight, flexible, and modular designs. We show that Reed-Solomon codes, and more generally linear codes, satisfy all of these mathematical properties. We further demonstrate the power of this technique with Reed-Solomon-based biological experiments. We provide general purpose tools for experimentalists to construct and carry out practical pooling designs with rigorous guarantees for large screens.