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Bias Correction in Estimating Proportions by Imperfect Pooled Testing

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  • Graham Hepworth

    (The University of Melbourne)

  • Brad J. Biggerstaff

    (Centers for Disease Control and Prevention)

Abstract

In the estimation of proportions by pooled testing, the MLE is biased. Hepworth and Biggerstaff (JABES, 22:602–614, 2017) proposed an estimator based on the bias correction method of Firth (Biometrika 80:27–38, 1993) and showed that it is almost unbiased across a range of pooled testing problems involving no misclassification. We now extend their work to allow for imperfect testing. We derive the estimator, provide a Newton–Raphson iterative formula for its computation and test it in situations involving equal or unequal pool sizes, drawing on problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses. Our estimator is highly effective at reducing the bias for prevalences consistent with the pooled testing procedure employed.

Suggested Citation

  • Graham Hepworth & Brad J. Biggerstaff, 2021. "Bias Correction in Estimating Proportions by Imperfect Pooled Testing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 90-104, March.
    • Handle: RePEc:spr:jagbes:v:26:y:2021:i:1:d:10.1007_s13253-020-00411-5
    DOI: 10.1007/s13253-020-00411-5
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    References listed on IDEAS

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    1. Graham Hepworth & Brad J. Biggerstaff, 2017. "Bias Correction in Estimating Proportions by Pooled Testing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 602-614, December.
    2. Graham Hepworth & Ray Watson, 2009. "Debiased estimation of proportions in group testing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 105-121, February.
    3. 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.
    4. Aiyi Liu & Chunling Liu & Zhiwei Zhang & Paul S. Albert, 2012. "Optimality of group testing in the presence of misclassification," Biometrika, Biometrika Trust, vol. 99(1), pages 245-251.
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