Constructions and Comparisons of Pooling Matrices for Pooled Testing of COVID-19

TL;DR

This paper introduces a new family of pooling matrices for COVID-19 pooled testing, compares their performance with existing matrices, and highlights the importance of selecting the appropriate matrix based on prevalence rates.

Contribution

The paper proposes a novel family of pooling matrices derived from finite projective planes and demonstrates their adaptability and potential advantages over existing matrices in pooled testing.

Findings

PPoL matrices can dynamically adjust to prevalence rates.

No single pooling matrix is optimal across all prevalence rates.

Proper matrix selection improves testing efficiency.

Abstract

In comparison with individual testing, group testing (also known as pooled testing) is more efficient in reducing the number of tests and potentially leading to tremendous cost reduction. As indicated in the recent article posted on the US FDA website, the group testing approach for COVID-19 has received a lot of interest lately. There are two key elements in a group testing technique: (i) the pooling matrix that directs samples to be pooled into groups, and (ii) the decoding algorithm that uses the group test results to reconstruct the status of each sample. In this paper, we propose a new family of pooling matrices from packing the pencil of lines (PPoL) in a finite projective plane. We compare their performance with various pooling matrices proposed in the literature, including 2D-pooling, P-BEST, and Tapestry, using the two-stage definite defectives (DD) decoding algorithm. By conducting extensive simulations for a range of prevalence rates up to 5%, our numerical results show that there is no pooling matrix with the lowest relative cost in the whole range of the prevalence rates. To optimize the performance, one should choose the right pooling matrix, depending on the prevalence rate. The family of PPoL matrices can dynamically adjust their column weights according to the prevalence rates and could be a better alternative than using a fixed pooling matrix.