Abstract
We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436–440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.
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Aprahamian, H., Bish, D.R., Bish, E.K.: Residual risk and waste in donated blood with pooled nucleic acid testing. Stat. Med. 35(28), 5283–5301 (2016)
Aprahamian, H., Bish, D.R., Bish, E.K.: Optimal risk-based group testing. Manag. Sci. 65(9), 4365–4384 (2019)
Augenblick, N., Kolstad, J.T., Obermeyer, Z., Wang, A.: Group testing in a pandemic: The role of frequent testing, correlated risk, and machine learning. Technical report, National Bureau of Economic Research (2020)
Black, M.S., Bilder, C.R., Tebbs, J.M.: Group testing in heterogeneous populations by using halving algorithms. J. R. Stat. Soc. Ser. C (Appl. Stat.) 61(2), 277–290 (2012)
Black, M.S., Bilder, C.R., Tebbs, J.M.: Optimal retesting configurations for hierarchical group testing. J. R. Stat. Soc. Ser. C (Appl. Stat.) 64(4), 693–710 (2015)
Cherif, A., Grobe, N., Wang, X., Kotanko, P.: Simulation of pool testing to identify patients with coronavirus disease 2019 under conditions of limited test availability. JAMA Netw. Open 3(6), e2013075–e2013075 (2020)
Deb, R., Pai, M., Vohra, A., Vohra, R.: Testing alone is insufficient. Rev. Econ. Design 26(1), 1–21 (2022)
Dorfman, R.: The detection of defective members of large populations. Ann. Math. Stat. 14(4), 436–440 (1943)
Du, D., Hwang, F.K.: Combinatorial Group Testing and Its Applications, vol. 12. World Scientific, Singapore (2000)
Ely, J., Galeotti, A., Jann, O., Steiner, J.: Optimal test allocation. J. Econ. Theory 193, 105236 (2021). https://doi.org/10.1016/j.jet.2021.105236
Finucan, H.: The blood testing problem. J. R. Stat. Soc. Ser. C (Appl. Stat.) 13(1), 43–50 (1964)
Gollier, C., Gossner, O.: Group testing against covid-19. Covid Econ. 2 (2020)
Hwang, F.: A generalized binomial group testing problem. J. Am. Stat. Assoc. 70(352), 923–926 (1975)
Lipnowski, E., Ravid, D.: Pooled testing for quarantine decisions. J. Econ. Theory 198, 105372 (2021). https://doi.org/10.1016/j.jet.2021.105372
Makris, M.: Covid and social distancing with a heterogenous population. Econ. Theory (2021). https://doi.org/10.1007/s00199-021-01377-2
Sterrett, A.: On the detection of defective members of large populations. Ann. Math. Stat. 28(4), 1033–1036 (1957)
Vohra, R.V.: Mechanism Design: A Linear Programming Approach, vol. 47. Cambridge University Press, Cambridge (2011)
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We thank Bob Barbera, Olivier Gossner, Eric Schliesser, a referee, the Editor, and participants at HKBU, Kyoto KIER, NTU, Osaka ISER and Sinica joint seminar, Georgetown, Bonn, Kansas Workshop in Economic Theory, Glasgow and Rice theory group meeting for very helpful comments and suggestions. Eraslan gratefully acknowledges support from National Science Foundation under Grant SES-1730636. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
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Bobkova, N., Chen, Y. & Eraslan, H. Optimal group testing with heterogeneous risks. Econ Theory 77, 413–444 (2024). https://doi.org/10.1007/s00199-023-01502-3
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DOI: https://doi.org/10.1007/s00199-023-01502-3
Keywords
- Group testing
- Pooled testing
- Positive assortative matching
- Negative assortative matching
- Heterogeneous risks