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A Note on the Minimax Solution for the Two-Stage Group Testing Problem

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  • Yaakov Malinovsky
  • Paul S. Albert

Abstract

Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations, the exact value of the probability p of being affected is unknown. We present both minimax and Bayesian solutions for the group size problem when p is unknown. For unbounded p , we show that the minimax solution for group size is 8, while using a Bayesian strategy with Jeffreys' prior results in a group size of 13. We also present solutions when p is bounded from above. For the practitioner, we propose strong justification for using a group size of between 8 and 13 when a constraint on p is not incorporated and provide useable code for computing the minimax group size under a constrained p .

Suggested Citation

  • Yaakov Malinovsky & Paul S. Albert, 2015. "A Note on the Minimax Solution for the Two-Stage Group Testing Problem," The American Statistician, Taylor & Francis Journals, vol. 69(1), pages 45-52, February.
    • Handle: RePEc:taf:amstat:v:69:y:2015:i:1:p:45-52
    DOI: 10.1080/00031305.2014.983545
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    References listed on IDEAS

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    1. James O. Berger & Jose M. Bernardo & Dongchu Sun, 2012. "Objective Priors for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 636-648, June.
    2. Joshua M. Tebbs & Christopher S. McMahan & Christopher R. Bilder, 2013. "Two-Stage Hierarchical Group Testing for Multiple Infections with Application to the Infertility Prevention Project," Biometrics, The International Biometric Society, vol. 69(4), pages 1064-1073, December.
    3. 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.
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