Effective Matrix Designs for COVID-19 Group Testing

Abstract

Background: Grouping samples with low prevalence of positives into pools and testing these pools can achieve considerable savings in testing resources compared with individual testing in the context of COVID-19. We review published pooling matrices, which encode the assignment of samples into pools and describe decoding algorithms, which decode individual samples from pools. Based on the findings we propose new one-round pooling designs with high compression that can efficiently be decoded by combinatorial algorithms. This expands the admissible parameter space for the construction of pooling matrices compared to current methods. Results: By arranging samples in a grid and using polynomials to construct pools, we develop direct formulas for an Algorithm (Polynomial Pools (PP)) to generate assignments of samples into pools. Designs from PP guarantee to correctly decode all samples with up to a specified number of positive samples. PP includes recent combinatorial methods for COVID-19, and enables new constructions that can result in more effective designs. Conclusion: For low prevalences of COVID-19, group tests can save resources when compared to individual testing. Constructions from the recent literature on combinatorial methods have gaps with respect to the designs that are available. We develop a method (PP), which generalizes previous constructions and enables new designs that can be advantageous in various situations.

Effective matrix designs for COVID-19 group testing

“…The degree of the polynomial is and a sample is represented with a pair of coordinates . When our method is analogous to the incidence matrix of an affine plane [ 6 , VII.2.2], [ 19 ] and the polynomials reduce to lines. For a prime number the computations can be done using modulus arithmetic.…”

Effective Matrix Designs for COVID-19 Group Testing

“…The degree of the polynomial is d − 1 and a sample is represented with a pair of coordinates v = ( x, y ). When d = 2 our method is analogous to the incidence matrix of an affine plane [6, VII.2.2], [19] and the polynomials reduce to lines. For p = q a prime number the computations can be done using modulus arithmetic.…”