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. 2023 Jun 6:1–32. Online ahead of print. doi: 10.1007/s00199-023-01502-3

Optimal group testing with heterogeneous risks

Nina Bobkova 1, Ying Chen 2,✉, Hülya Eraslan 3,4
PMCID: PMC10243685  PMID: 37360771

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.

Keywords: Group testing, Pooled testing, Positive assortative matching, Negative assortative matching, Heterogeneous risks

Footnotes

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.

Publisher's Note

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Contributor Information

Nina Bobkova, Email: nina.bobkova@rice.edu.

Ying Chen, Email: ying.chen@jhu.edu.

Hülya Eraslan, Email: eraslan@rice.edu.

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