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Abstract

Economic impact of composite sampling is investigated in the realistic framework of tests with positive probability of false positive and of false negative results. Sensitivity and specificity when pooling samples are also discussed, using rarefaction as a framework.

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References

  1. Boswell, M.T., Gore, S.D., Lovison, G., Patil, G.P.: Annotated bibliography of composite sampling, Part A: 1936–92. Environ. Ecol. Stat. 3, 1–50 (1996)

    Google Scholar 

  2. Dorfman, R.: The detection of defective members in large populations. Ann. Math. Stat. 14, 436–440 (1943)

    Google Scholar 

  3. Finucan, H.M.: The blood testing problem. Appl. Stat. J. Roy. Stat. C 13, 43–50 (1964)

    Google Scholar 

  4. Gill, A., Gottlieb, D.: The identification of a set by successive intersections. In: Information and Control, pp. 20–25. Ellis Horwood, Chichester (1974)

    Google Scholar 

  5. Hess, K.T., Liewald, A., Schmidt, K.D.: An extension of Panjer’s recursion. Astin Bull. 32(2), 283–297 (2002)

    Google Scholar 

  6. Hung, M., Swallow, W.: Robustness of group testing in the estimation of proportions. Biometrics 55, 231–237 (1999)

    Google Scholar 

  7. Hwang, F.K.: Group testing with a dilution effect. Biometrika 63, 671–673 (1976)

    Google Scholar 

  8. Kim, H., Hudgens, M., Dreyfuss, J., Westreich, D., Pilcher, C.: Comparison of group testing algorithms for case identification in the presence of testing errors. Biometrics 63, 1152–1163 (2007)

    Google Scholar 

  9. Liu, S.C., Chiang, K.S., Lin, C.H., Chung, W.C., Lin, S.H., Yang, T.C.: Cost analysis in choosing group size when group testing for Potato virus Y in the presence of classification errors. Ann. Appl. Biol. 159, 491–502 (2011)

    Google Scholar 

  10. Sterret, A.: On the detection of defective members of large populations. Ann. Math. Stat. 28, 1033–1036 (1957)

    Google Scholar 

  11. Sobel, M., Elashoff, R.: Group testing with a new goal, estimation. Biometrika 62, 181–193 (1975)

    Google Scholar 

  12. Tu, X.M., Litvak, E., Pagano, M.: Studies of AIDS and HIV surveillance, Screening tests: Can we get more by doing less? Stat. Med. 13, 1905–1919 (1994)

    Google Scholar 

  13. Tu, X.M., Litvak, E., Pagano, M.: On the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease: Application to HIV screening. Biometrika 82(2), 287–297 (1995)

    Google Scholar 

  14. Wein, L., Zenios, S.: Pooled testing for HIV screening: capturing the dilution effect. Oper. Res. 44, 543–569 (1996)

    Google Scholar 

  15. Williams, D.: Weighing the Odds: A Course in Probability and Statistics. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  16. Zenios, S., Wein, L.: Pooled testing for HIV prevalence estimation exploiting the dilution effect. Stat. Med. 17, 1447–1467 (1998)

    Google Scholar 

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Acknowledgements

The authors thank the referees for their very useful comments. This research has been supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011, and PTDC/FEDER.

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Correspondence to Rui Santos .

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Santos, R., Pestana, D., Martins, J.P. (2013). Extensions of Dorfman’s Theory. In: Oliveira, P., da Graça Temido, M., Henriques, C., Vichi, M. (eds) Recent Developments in Modeling and Applications in Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32419-2_19

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