Abstract
The maximum likelihood estimator for estimating proportions by group testing is biased. An expression for the approximate bias has been previously presented, which enables the creation of a less biased estimator by removing the term of \(O(n^{-1})\). However, in this previous work the term of \(O(n^{-2})\) was incorrectly derived. This note gives a correct derivation, and examines the relative contribution of the two terms.
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References
Burrows PM (1987) Improved estimation of pathogen transmission rates by group testing. Phytopathology 77:363–365
Colon S, Patil GP, Taillie C (2001) Estimating prevalence using composites. Environ Ecol Stat 8:213–236
Crockett RK, Burkhalter K, Mead D, Kelly R, Brown J, Vernado W, Roy A, Horiuchi K, Biggerstaff BJ, Miller B, Nasci R (2012) Culex Flavivirus and West Nile Virus in Culex quinquefasciatus populations in the southeastern United States. J Med Entomol 49:165–174
Gart JJ (1991) An application of score methodology: confidence intervals and tests of fit for one-hit curves. In: Rao CR, Chakraborty R (eds) Handbook of statistics, vol 8. Elsevier, Amsterdam, pp 395–406
Gibbs AJ, Gower JC (1960) The use of a multiple-transfer method in plant virus transmission studies—some statistical points arising in the analysis of results. Ann Appl Biol 48:75–83
Hepworth G, Watson R (2009) Debiased estimation of proportions in group testing. J R Stat Soc C Appl 58:105–121
Johnson NL, Kemp AW, Kotz S (2005) Univariate discrete distributions, 3rd edn. Wiley, New York
Keys JR, Leone PA, Eron JJ, Alexander K, Brinson M, Swanstrom R (2014) Large scale screening of human sera for HCV RNA and GBV-C RNA. J Med Virol 86:473–477
Liu C, Liu A, Zhang B, Zhang Z (2013) Improved confidence intervals of a small probability from pooled testing with misclassification. Front Public Health. doi:10.3389/fpubh.2013.00039
Lovison G, Gore SD, Patil GP (1994) Design and analysis of composite sampling procedures: a review. In: Patil GP, Rao CR (eds) Handbook of statistics, vol 12. Elsevier, Amsterdam, pp 103–166
Montesinos-Lopez OA, Montesinoz-Lopez A, Crossa J, Eskridge K, Saenz RA (2011) Optimal sample size for estimating the proportion of transgenic plants using the Dorfman model with a random confidence interval. Seed Sci Res 21:235–245
Patil GP (2011) Composite sampling: a novel method to accomplish observational economy in environmental studies: a monograph introduction. Environ Ecol Stat 18:385–392
Schaarschmidt F (2007) Experimental design for one-sided confidence intervals or hypothesis tests in binomial group testing. Commun Biom Crop Sci 2:32–40
Swallow WH (1985) Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology 75:882–889
Tebbs JM, McMahan CS, Bilder CR (2013) Two-stage hierarchical group testing for multiple infections with application to the infertility prevention project. Biometrics 69:1064–1073
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Hepworth, G. Approximate bias of the estimated proportion in group testing. Environ Ecol Stat 24, 1–6 (2017). https://doi.org/10.1007/s10651-016-0358-7
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DOI: https://doi.org/10.1007/s10651-016-0358-7