Composite Sampling pp 81-86 | Cite as

# Estimating Prevalence of a Trait

## 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.

## Keywords

Composite Sample Maximum Likelihood Estimator Sampling Unit Unbiased Estimator Taylor Series Expansion## Bibliography

- Anscombe, F. J. (1956). On estimating binomial response relations. Biometrika 43:461–464.MATHMathSciNetGoogle Scholar
- 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.Google Scholar
- Boswell, M. T. and Patil, G. P. (1987). A perspective of composite sampling. Commun. Stat. Theor. Methods 16:3069–3093.CrossRefGoogle Scholar
- Burrows, P. M. (1987). Improved estimation of pathogen transmission rates by group testing. Phytopathology 77:363–365.CrossRefGoogle Scholar
- Chiang, C. L. and Reeves, W. C. (1962). Statistical estimation of virus infection rates in mosquito vector populations. Am. J. Hygiene 75:377–391.Google Scholar
- Fisher, R. A. (1921). On the mathematical foundations of theoretical statistics. Phil. Trans. (A) 222:309–368.Google Scholar
- 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.Google Scholar - Garner, F. C., Stapanian, M. A., Yfantis, E. A., and Williams, L. R. (1990). Probability estimation with sample compositing techniques. MS.Google Scholar
- 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.CrossRefGoogle Scholar
- Griffiths, D. A. (1972). A further note on the probability of disease transmission. Biometrics 28:1133–1139.CrossRefGoogle Scholar
- Haldane, J. B. S. (1955). The estimation and significance of the logarithm of a ratio of frequencies. Ann. Hum. Genet. 20:309–311.CrossRefGoogle Scholar
- Kerr, J. D. (1971). The probability of disease transmission. Biometrics 27:219–222.CrossRefGoogle Scholar
- Loyer, M. W. (1983). Bad probability, good statistics, and group testing for binomial estimation. Am. Stat. 37:57–59.CrossRefGoogle Scholar
- Sobel, M. and Elashoff, R. M. (1975). Group testing with a new goal, estimation. Biometrika 62:181–193.MATHCrossRefMathSciNetGoogle Scholar
- Swallow, W. H. (1985). Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology 75:882–889.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- Thompson, K. H. (1962). Estimation of the proportion of vectors in a natural population of insects. Biometrics 18:568–578.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar