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Pool testing with dilution effects and heterogeneous priors

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  • Gustavo Quinderé Saraiva

    (Business School, Pontificia Universidad Católica de Chile)

Abstract

The Dorfman pooled testing scheme is a process in which individual specimens (e.g., blood, urine, swabs, etc.) are pooled and tested together; if the merged sample tests positive for infection, then each specimen from the pool is tested individually. Through this procedure, laboratories can reduce the expected number of tests required to screen the population, as individual tests are only carried out when the pooled test detects an infection. Several different partitions of the population can be used to form the pools. In this study, we analyze the performance of ordered partitions, those in which subjects with similar probability of infection are pooled together. We derive sufficient conditions under which ordered partitions outperform other types of partitions in terms of minimizing the expected number of tests, the expected number of false negatives, and the expected number of false positive classifications. These sufficient conditions can be easily verified in practical applications once the dilution effect has been estimated. We also propose a measure of equity and present conditions under which this measure is maximized by ordered partitions.

Suggested Citation

  • Gustavo Quinderé Saraiva, 2023. "Pool testing with dilution effects and heterogeneous priors," Health Care Management Science, Springer, vol. 26(4), pages 651-672, December.
    • Handle: RePEc:kap:hcarem:v:26:y:2023:i:4:d:10.1007_s10729-023-09650-7
    DOI: 10.1007/s10729-023-09650-7
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    References listed on IDEAS

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    1. Leonardo J. Basso & Marcel Goic & Marcelo Olivares & Denis Sauré & Charles Thraves & Aldo Carranza & Gabriel Y. Weintraub & Julio Covarrubia & Cristian Escobedo & Natalia Jara & Antonio Moreno & Demia, 2023. "Analytics Saves Lives During the COVID-19 Crisis in Chile," Interfaces, INFORMS, vol. 53(1), pages 9-31, January.
    2. Mark Schneider & Byung‐Cheol Kim, 2020. "The utilitarian–maximin social welfare function and anomalies in social choice," Southern Economic Journal, John Wiley & Sons, vol. 87(2), pages 629-646, October.
    3. Lawrence M. Wein & Stefanos A. Zenios, 1996. "Pooled Testing for HIV Screening: Capturing the Dilution Effect," Operations Research, INFORMS, vol. 44(4), pages 543-569, August.
    4. Christopher S. McMahan & Joshua M. Tebbs & Christopher R. Bilder, 2012. "Informative Dorfman Screening," Biometrics, The International Biometric Society, vol. 68(1), pages 287-296, March.
    5. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.
    6. Hrayer Aprahamian & Ebru K. Bish & Douglas R. Bish, 2018. "Adaptive risk-based pooling in public health screening," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 753-766, September.
    7. Walter Bossert & Kohei Kamaga, 2020. "An axiomatization of the mixed utilitarian–maximin social welfare orderings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 451-473, March.
    8. Hae-Young Kim & Michael G. Hudgens & Jonathan M. Dreyfuss & Daniel J. Westreich & Christopher D. Pilcher, 2007. "Comparison of Group Testing Algorithms for Case Identification in the Presence of Test Error," Biometrics, The International Biometric Society, vol. 63(4), pages 1152-1163, December.
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