Cutting testing costs by the pooling design

Keywords: pooling design, group testing, Hwang’s generalized binary-splitting algorithm, matrix strategy, COVID-19, SARS-CoV-2

Abstract


Introduction/purpose: The purpose of group testing algorithms is to provide a more rational resource usage. Therefore, it is expected to improve the efficiency of large–scale COVID-19 screening as well.

Methods: Two variants of non–adaptive group testing approaches are presented: Hwang’s generalized binary–splitting algorithm and the matrix strategy.

Results: The positive and negative sides of both approaches are discussed. Also, the estimations of the maximum number of tests are given. The matrix strategy is presented with a particular modification which reduces the corresponding estimation of the maximum number of tests and which does not affect the complexity of the procedure. This modification can be interesting from the applicability viewpoint.

Conclusion: Taking into account the current situation, it makes sense to consider these methods in order to achieve some resource cuts in testing, thus making the epidemiological measures more efficient than they are now.

Author Biography

Dimitrije D. Čvokić, University of Banja Luka, Faculty of Sciences and Mathematics, Banja Luka, Republic of Srpska, Bosnia and Herzegovina

Одсјек за математику и информатику

Виши асистент

References

-Blic. 2020. Nema testova, ima testova, u čemu je problem? Blic, 4 July [online]. Available at: www.blic.rs/vesti/drustvo/pcr-test-korona-virus-uzice-beograddr-predrag-kon/kbb68g9 (in Serbian) [Accessed 15 July 2020].

Colbourn, C.J. & Dinitz, J.H. 2007. Handbook of Combinatorial Designs (2nd ed.). Boca Raton: Chapman & Hall/ CRC. p. 574, Section 46: Pooling Designs Ding-Zhu, Du. & Hwang, F.K. 1993. Combinatorial group testing and its applications. Singapore: World Scientific. ISBN 978-9810212933.

Dodd, R., Notari, E. & Stramer, S. 2002. Current prevalence and incidence of infectious disease markers and estimated window-period risk in the American Red Cross blood donor population. Transfusion, 42(8), pp.975-979. Available at: https://doi.org/10.1046/j.1537-2995.2002.00174.x.

Dorfman, R. 1943. The Detection of Defective Members of Large Populations. Annals of Mathematical Statistics, 14(4), pp.436-440. Available at: https://doi.org/10.1214/aoms/1177731363.

Eberhardt, J.N., Breuckmann, N.P. & Eberhardt, C.S. 2020. Multi-Stage Group Testing Improves Efficiency of Large-Scale COVID-19 Screening. Journal of Clinical Virology, 128(art.number:104382). Available at: https://doi.org/10.1016/j.jcv.2020.104382.

-Faculty of Electrical Engineering in Banja Luka. 2020. Ukupan broj slučajeva u Republici Srpskoj. [online] Available at: https://covid19.etfbl.net/ (in Serbian) [Accessed 15 July 2020].

Gaydos, C.A. 2005. Nucleic Acid Amplification Tests for Gonorrhea and Chlamydia: Practice and Applications. Infectious Disease Clinics of North America, 19(2), pp.367-386. Available at: https://doi.org/10.1016/j.idc.2005.03.006.

Gollier, C. & Gossner, O. 2020. Group testing against Covid-19. Covid Economics, 1(2), pp.32-42 [online]. Available at: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/by/gollier/covid_economics.pdf [Accessed: 21 August 2020].

-Government of Republic of Serbia. 2020. COVID19 Statistics in Serbia [online] Available at: https://covid19.data.gov.rs/?locale=en [Accessed 25 July 2020].

-Government of Republic of Srpska. 2020. Zeljkovic: Nastavlja se trend pogoršanja epidemiološke situacije [online]. Available at: https://koronavirususrpskoj.com/nastavlja-se-trend-pogorsanja-epidemioloske-situacije/ (in Serbian) [Accessed 25 July 2020] (In the original: -Влада Републике Српске. 2020. Зељковић: Наставља се тренд погоршања епидемиолошке ситуације).

Mallapaty, S. 2020. The Mathematical Strategy That Could Transform Coronavirus Testing. Nature, 10 July [online]. Available at: https://www.nature.com/articles/d41586-020-02053-6 [Accessed 15 July 2020].

McMahan, C.S., Tebbs, J.M. & Bilder, C.R. 2012. Two-Dimensional Informative Array Testing. Biometrics, 68(3), pp.793-804. Available at: https://doi.org/10.1111/j.1541-0420.2011.01726.x.

Pfeiffer, S., Anderson, M. & van Woerkom, B. 2020. Despite Early Warnings, U.S. Took Months To Expand Swab Production For COVID-19 Test. NPR [online]. Available at: https://www.npr.org/2020/05/12/853930147/despite-early-warnings-u-s-took-months-to-expand-swab-production-for-covid-19-te [Accessed 15 July 2020].

Phatarfod, R.M. & Sudbury, A. 1994. The use of a square array scheme in blood testing. Statistics in Medicine, 13(22), pp.2337-2343. Available at: https://doi.org/10.1002/sim.4780132205.

Sanche, S., Lin, Y., Xu, C., Romero-Severson, E., Hengartner, N. & Ke, R. 2020. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerging Infectious Diseases 26(7), pp.1470-1477. Available at: https://dx.doi.org/10.3201/eid2607.200282.

White, D., Kramer, L., Backenson, P., Lukacik, G., Johnson, G., Oliver, J., Howard, J., Means, R., Eidson, M., Gotham, I., Kulasekera, V. & Campbell, S. 2001. Mosquito surveillance and polymerase chain reaction detection of West Nile Virus, New York state. Emerging Infectious Diseases, 7(4), pp.643-649. Available at: https://dx.doi.org/10.3201/eid0704.017407.

Published
2020/07/25
Section
Original Scientific Papers