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Debiased estimation of proportions in group testing

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  • Graham Hepworth
  • Ray Watson

Abstract

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. Copyright (c) 2009 Royal Statistical Society.

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.
  • Handle: RePEc:bla:jorssc:v:58:y:2009:i:1:p:105-121
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2008.00639.x
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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. repec:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0297-2 is not listed on IDEAS

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