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Optimal group testing with heterogeneous risks

Author

Listed:
  • Nina Bobkova

    (Rice University and CEPR)

  • Ying Chen

    (Johns Hopkins University)

  • Hülya Eraslan

    (Rice University and NBER
    Osaka University)

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.

Suggested Citation

  • Nina Bobkova & Ying Chen & Hülya Eraslan, 2024. "Optimal group testing with heterogeneous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 413-444, February.
    • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01502-3
    DOI: 10.1007/s00199-023-01502-3
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    References listed on IDEAS

    as
    1. Ned Augenblick & Jonathan T. Kolstad & Ziad Obermeyer & Ao Wang, 2020. "Group Testing in a Pandemic: The Role of Frequent Testing, Correlated Risk, and Machine Learning," NBER Working Papers 27457, National Bureau of Economic Research, Inc.
    2. Hrayer Aprahamian & Douglas R. Bish & Ebru K. Bish, 2019. "Optimal Risk-Based Group Testing," Management Science, INFORMS, vol. 65(9), pages 4365-4384, September.
    3. Lipnowski, Elliot & Ravid, Doron, 2021. "Pooled testing for quarantine decisions," Journal of Economic Theory, Elsevier, vol. 198(C).
    4. Ely, Jeffrey & Galeotti, Andrea & Jann, Ole & Steiner, Jakub, 2021. "Optimal test allocation," Journal of Economic Theory, Elsevier, vol. 193(C).
    5. Rahul Deb & Mallesh Pai & Akhil Vohra & Rakesh Vohra, 2022. "Testing alone is insufficient," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 1-21, March.
    6. H. M. Finucan, 1964. "The Blood Testing Problem," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 13(1), pages 43-50, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Group testing; Pooled testing; Positive assortative matching; Negative assortative matching; Heterogeneous risks;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D0 - Microeconomics - - General
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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