[Paper Review] Comparisons of Pooling Matrices for Pooled Testing of COVID-19.

Yi-Jheng Lin, Che-Hao Yu+3 more|arXiv (Cornell University)|Sep 30, 2020

SARS-CoV-2 detection and testing20 references4 citations

TL;DR

This paper proposes a new family of pooling matrices, Pencil of Lines in a Finite Projective Plane (PPoL), for pooled testing of COVID-19. Using the two-stage Definite Defectives (DD) decoding algorithm, simulations show that PPoL matrices dynamically adjust column weights to prevalence rates, outperforming fixed matrices like 2D-pooling, P-BEST, and Tapestry across varying prevalence levels up to 5%.

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.

Motivation & Objective

• To address the challenge of optimizing pooled testing efficiency in low-prevalence settings like early-stage COVID-19 screening.
• To design a flexible pooling matrix that adapts to varying prevalence rates rather than relying on fixed structures.
• To evaluate and compare the performance of PPoL matrices against existing pooling matrices under realistic testing conditions.
• To determine whether dynamic adjustment of column weights improves relative cost efficiency in pooled testing.

Proposed method

• Constructing pooling matrices using the geometric structure of the pencil of lines (PPoL) in a finite projective plane to ensure balanced and efficient sample pooling.
• Designing matrices with variable column weights that can be tuned according to estimated prevalence rates, enabling dynamic adaptation.
• Applying the two-stage Definite Defectives (DD) decoding algorithm to reconstruct individual sample statuses from group test results.
• Simulating pooled testing performance across a range of prevalence rates (up to 5%) using the PPoL matrices and comparing them with 2D-pooling, P-BEST, and Tapestry.
• Evaluating performance based on relative cost, defined as the ratio of total tests used to the number of samples tested.

Experimental results

Research questions

• RQ1 Can PPoL-based pooling matrices achieve lower relative cost than existing fixed pooling matrices across varying prevalence rates?
• RQ2 How does dynamic adjustment of column weights in PPoL matrices affect testing efficiency in low-prevalence scenarios?
• RQ3 Is there a single optimal pooling matrix across all prevalence rates, or does performance depend on the specific rate?
• RQ4 How do PPoL matrices compare to 2D-pooling, P-BEST, and Tapestry in terms of relative cost under the DD decoding algorithm?

Key findings

• No single pooling matrix achieves the lowest relative cost across all prevalence rates up to 5%, indicating that matrix choice must be prevalence-dependent.
• The PPoL family of matrices dynamically adjusts column weights based on prevalence, enabling better performance tuning than fixed matrices.
• PPoL matrices outperform 2D-pooling, P-BEST, and Tapestry in specific prevalence ranges, demonstrating superior adaptability and efficiency.
• The two-stage DD decoding algorithm effectively reconstructs individual statuses when used with PPoL matrices, ensuring high accuracy in low-prevalence settings.
• Simulations confirm that PPoL matrices reduce relative cost more effectively than fixed matrices when prevalence is known or estimated in advance.