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Nonparametric estimation of distributions and diagnostic accuracy based on group‐tested results with differential misclassification

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  • Wei Zhang
  • Aiyi Liu
  • Qizhai Li
  • Paul S. Albert

Abstract

This article concerns the problem of estimating a continuous distribution in a diseased or nondiseased population when only group‐based test results on the disease status are available. The problem is challenging in that individual disease statuses are not observed and testing results are often subject to misclassification, with further complication that the misclassification may be differential as the group size and the number of the diseased individuals in the group vary. We propose a method to construct nonparametric estimation of the distribution and obtain its asymptotic properties. The performance of the distribution estimator is evaluated under various design considerations concerning group sizes and classification errors. The method is exemplified with data from the National Health and Nutrition Examination Survey study to estimate the distribution and diagnostic accuracy of C‐reactive protein in blood samples in predicting chlamydia incidence.

Suggested Citation

  • Wei Zhang & Aiyi Liu & Qizhai Li & Paul S. Albert, 2020. "Nonparametric estimation of distributions and diagnostic accuracy based on group‐tested results with differential misclassification," Biometrics, The International Biometric Society, vol. 76(4), pages 1147-1156, December.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1147-1156
    DOI: 10.1111/biom.13236
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    References listed on IDEAS

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    1. 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.
    2. Christopher R. Bilder & Joshua M. Tebbs & Christopher S. McMahan, 2019. "Informative group testing for multiplex assays," Biometrics, The International Biometric Society, vol. 75(1), pages 278-288, March.
    3. Shih-Hao Huang & Mong-Na Lo Huang & Kerby Shedden & Weng Kee Wong, 2017. "Optimal group testing designs for estimating prevalence with uncertain testing errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1547-1563, November.
    4. Pengfei Li & Yukun Liu & Jing Qin, 2017. "Semiparametric Inference in a Genetic Mixture Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1250-1260, July.
    5. Delaigle, Aurore & Meister, Alexander, 2011. "Nonparametric Regression Analysis for Group Testing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 640-650.
    6. Peijie Hou & Joshua M. Tebbs & Christopher R. Bilder & Christopher S. McMahan, 2017. "Hierarchical group testing for multiple infections," Biometrics, The International Biometric Society, vol. 73(2), pages 656-665, June.
    7. M. Hung & William H. Swallow, 1999. "Robustness of Group Testing in the Estimation of Proportions," Biometrics, The International Biometric Society, vol. 55(1), pages 231-237, March.
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    Cited by:

    1. Md S. Warasi & Laura L. Hungerford & Kevin Lahmers, 2022. "Optimizing Pooled Testing for Estimating the Prevalence of Multiple Diseases," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 713-727, December.

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