Abstract
When sampling units selected from a population and measurements indicate presence or absence of a trait, it is possible to either classify every sampling unit as positive/negative or estimate the prevalence of the trait. The former is desired when the interest is in identifying all sampling units that test positive (and hence possess the trait). The latter is useful when the interest is not in the status of individual sampling units that possess the trait. The problem, then, is to estimate the sampling units in the population that possess the trait, when presence. Absence measurements are obtained on composite samples. Here, the values on the individual sampling units in the population are assumed to be independent and identically distributed random variables.
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Bibliography
Anscombe, F. J. (1956). On estimating binomial response relations. Biometrika 43:461–464.
Bartlett, M. S. (1935). Mathematical appendix to a paper, by G. E. Blackman, entitled “A study by statistical methods of the distribution of species in grassland associations.” Ann. Bot. 49:749–777.
Boswell, M. T. and Patil, G. P. (1987). A perspective of composite sampling. Commun. Stat. Theor. Methods 16:3069–3093.
Burrows, P. M. (1987). Improved estimation of pathogen transmission rates by group testing. Phytopathology 77:363–365.
Chiang, C. L. and Reeves, W. C. (1962). Statistical estimation of virus infection rates in mosquito vector populations. Am. J. Hygiene 75:377–391.
Fisher, R. A. (1921). On the mathematical foundations of theoretical statistics. Phil. Trans. (A) 222:309–368.
Garner, F. C., Stapanian, M. A., and Williams, L. R. (1988). Composite sampling for environmental monitoring. In Principles of Environmental Sampling, L. H. Keith, ed. American Chemical Society, Washington, DC. pp. 363–374.
Garner, F. C., Stapanian, M. A., Yfantis, E. A., and Williams, L. R. (1990). Probability estimation with sample compositing techniques. MS.
Gibbs, A. J. and Gower, J. C. (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.
Griffiths, D. A. (1972). A further note on the probability of disease transmission. Biometrics 28:1133–1139.
Haldane, J. B. S. (1955). The estimation and significance of the logarithm of a ratio of frequencies. Ann. Hum. Genet. 20:309–311.
Kerr, J. D. (1971). The probability of disease transmission. Biometrics 27:219–222.
Loyer, M. W. (1983). Bad probability, good statistics, and group testing for binomial estimation. Am. Stat. 37:57–59.
Sobel, M. and Elashoff, R. M. (1975). Group testing with a new goal, estimation. Biometrika 62:181–193.
Swallow, W. H. (1985). Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology 75:882–889.
Swallow, W. H. (1987). Relative mean squared error and cost considerations in choosing group size for group testing to estimate infection rates and probabilities of disease transmission. Phytopathology 77:1376–1381.
Thompson, K. H. (1962). Estimation of the proportion of vectors in a natural population of insects. Biometrics 18:568–578.
Watson, M. A. (1936). Factors affecting the amount of infection obtained by aphis transmission of the virus Hy. III. Philos. Trans. Roy. Soc. London, Ser. B. 226:457–489.
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Patil, G.P., Gore, S.D., Taillie*, C. (2011). Estimating Prevalence of a Trait. In: Composite Sampling. Environmental and Ecological Statistics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7628-4_4
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DOI: https://doi.org/10.1007/978-1-4419-7628-4_4
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