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Debiased estimation of proportions in group testing

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  • Graham Hepworth
  • Ray Watson

Abstract

Summary. In the assessment of disease, estimation of the proportion of infected units in a population can sometimes be facilitated by pooling units into groups for testing. Such group testing was used in a study of virus infection levels in carnation plants grown in glasshouses. In group testing problems, the maximum likelihood estimator is a biased estimator of the population proportion. We investigate the bias of the maximum likelihood estimator when testing groups of different size, using fixed and sequential procedures. The possibility of obtaining all positive groups contributes substantially to the bias. Analytical methods are shown to correct the bias for fixed procedures satisfactorily. For sequential procedures, with their uneven bias patterns, we propose a numerical method of correction which produces an almost unbiased estimator.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:1:p:105-121
    DOI: 10.1111/j.1467-9876.2008.00639.x
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    References listed on IDEAS

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    1. Joshua M. Tebbs, 2003. "Estimating ordered binomial proportions with the use of group testing," Biometrika, Biometrika Trust, vol. 90(2), pages 471-477, June.
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    Cited by:

    1. Xiong, Wenjun & Ding, Juan, 2015. "Robust procedures for experimental design in group testing considering misclassification," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 35-41.
    2. Shaul K. Bar‐Lev & Onno Boxma & Andreas Löpker & Wolfgang Stadje & Frank A. Van der Duyn Schouten, 2012. "Group testing procedures with quantitative features and incomplete identification," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 39-51, February.
    3. 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.
    4. 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.
    5. Nguyen, Ngoc T. & Bish, Ebru K. & Bish, Douglas R., 2021. "Optimal pooled testing design for prevalence estimation under resource constraints," Omega, Elsevier, vol. 105(C).
    6. 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.
    7. Jie Mi, 2019. "Some limit results in estimation of proportion based on group testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 1021-1038, November.

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    1. Nguyen, Ngoc T. & Bish, Ebru K. & Bish, Douglas R., 2021. "Optimal pooled testing design for prevalence estimation under resource constraints," Omega, Elsevier, vol. 105(C).
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