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Bias Correction in Estimating Proportions by Pooled Testing

Author

Listed:
  • 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, and several methods of correcting the bias have been presented in previous studies. We propose a new estimator based on the bias correction method introduced by Firth (Biometrika 80:27–38, 1993), which uses a modification of the score function, and we provide an easily computable, Newton–Raphson iterative formula for its computation. Our proposed estimator is almost unbiased across a range of problems, and superior to existing methods. We show that for equal pool sizes the new estimator is equivalent to the estimator proposed by Burrows (Phytopathology 77:363–365, 1987). The performance of our estimator is examined using pooled testing problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0297-2
    DOI: 10.1007/s13253-017-0297-2
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    References listed on IDEAS

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    1. Ron Brookmeyer, 1999. "Analysis of Multistage Pooling Studies of Biological Specimens for Estimating Disease Incidence and Prevalence," Biometrics, The International Biometric Society, vol. 55(2), pages 608-612, June.
    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. Shih-Chia Liu & Kuo-Szu Chiang & Cheng-Hsiang Lin & Ting-Chin Deng, 2011. "Confidence interval procedures for proportions estimated by group testing with groups of unequal size adjusted for overdispersion," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1467-1482, June.
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    Cited by:

    1. Gregory Haber & Yaakov Malinovsky, 2020. "On the Construction of Unbiased Estimators for the Group Testing Problem," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 220-241, February.
    2. 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.

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