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Sample size for detecting transgenic plants using inverse binomial group testing with dilution effect

Published online by Cambridge University Press:  11 July 2013

Osval Antonio Montesinos-López ,
Abelardo Montesinos-López ,
José Crossa  and
Kent Eskridge
Osval Antonio Montesinos-López
Affiliation:
Facultad de Telemática, Universidad de Colima, Bernal Díaz del Castillo No. 340, Col. Villas San Sebastián, C.P. 28045, Colima, Colima, México
Abelardo Montesinos-López
Affiliation:
Departamento de Estadística, Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Guanajuato, México
José Crossa*
Affiliation:
Biometrics and Statistics Unit, Maize and Wheat Improvement Center (CIMMYT), Apdo, Postal 6-641, Mexico, D.F., Mexico
Kent Eskridge
Affiliation:
Department of Statistics, University of Nebraska, Lincoln, Nebraska, USA
*
*Correspondence Email: [email protected]
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Abstract

In this study we developed a sample size procedure for estimating the proportion of genetically modified plants (adventitious presence of unwanted transgenic plants, AP) under inverse negative binomial group testing sampling, which guarantees that exactly r positive pools will be present in the sample. To achieve this aim, pools are drawn one by one until the sample contains r positive pools. The use of group testing produces significant savings because groups that contain several units (plants) are analysed without having to inspect individual plants. However, when using group testing we need to consider an appropriate pool size (k) because if the k individuals that form a pool are mixed and homogenized, the AP will be diluted. This effect increases with the size of the pool; it may also decrease the AP concentration in the pool below the laboratory test detection limit (d), thereby increasing the number of false negatives. The method proposed in this study determines the required sample size considering the dilution effect and guarantees narrow confidence intervals. In addition, we derived the maximum likelihood estimator of p and an exact confidence interval (CI) under negative binomial pool testing considering the detection limit of the laboratory test, d, and the concentration of AP per unit (c). Simulated data were created and tables presented showing different potential scenarios that a researcher may encounter. We also provide an R program that can be used to create other scenarios.

Keywords

adventitious presence of transgenic plants (AP)dilution effectinverse samplingnegative binomial pool testingsample size
Type
Research Papers
Information
Seed Science Research , Volume 23 , Issue 4 , December 2013 , pp. 279 - 288
Copyright
Copyright © Cambridge University Press 2013 

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References

Bhattacharyya, G.K., Karandinos, M.G. and Defoliart, G.R. (1979) Point estimates and CIs for infection rates using pooled organisms in epidemiologic studies. American Journal of Epidemiology 109, 124–131.CrossRefGoogle Scholar
Bilder, C.R. (2009) Human or Cylon? Group testing on Battlestar Galáctica. Chance 223, 46–50.Google Scholar
Chiang, C.L. and Reeves, W.C. (1962) Statistical estimation of virus infection rates in mosquito vector populations. American Journal of Hygiene 75, 377–391.Google ScholarPubMed
Cleveland, D.A., Soleri, D., Aragón-Cuevas, F., Crossa, J. and Gepts, P. (2005) Detecting (trans)gene flow to landraces in centers of crop origin: lessons from the case of maize in Mexico. Environmental Biosafety Research 4, 197–208.CrossRefGoogle ScholarPubMed
Cohen, J. (1994) The earth is round (p < 0.05). American Psychologist 49, 997–1003.CrossRefGoogle Scholar
Dodd, R., Notari, E. and Stramer, S. (2002) Current prevalence and incidence of infectious disease markers and estimated window-period risk in the American Red Cross donor population. Transfusion 42, 975–979.CrossRefGoogle Scholar
Dorfman, R. (1943) The detection of defective members of large populations. Annals of Mathematical Statistics 14, 436–440.CrossRefGoogle Scholar
Dyer, G.A., Serratos-Hernández, J.A., Perales, H.R., Gepts, P., Piñeyro-Nelson, A., Chavez, A., Salinas-Arreortua, N., Yúnez-Naude, A., Taylor, J.E. and Alvarez-Buylla, E.R. (2009) Dispersal of transgenes through maize seed systems in Mexico. PLoS ONE 4, e5734.CrossRefGoogle ScholarPubMed
Haldane, J.B. (1945) On a method of estimating frequencies. Biometrika 33, 222–225.CrossRefGoogle ScholarPubMed
Hernández-Suárez, C.M., Montesinos-López, O.A., McLaren, G. and Crossa, J. (2008) Probability models for detecting transgenic plants. Seed Science Research 18, 77–89.CrossRefGoogle Scholar
Kelley, K. (2007) Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach. Behavior Research Methods 39, 755–766.CrossRefGoogle ScholarPubMed
Kelley, K. and Maxwell, S.E. (2003) Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods 8, 305–321.CrossRefGoogle Scholar
Kelley, K. and Rausch, J.R. (2011) Sample size planning for longitudinal models: Accuracy in parameter estimation for polynomial change parameters. Psychological Methods 6, 391–405.CrossRefGoogle Scholar
Montesinos-López, O.A., Montesinos-López, A., Crossa, J., Eskridge, K. and Hernández-Suárez, C.M. (2010) Sample size for detecting and estimating the proportion of transgenic plants with narrow confidence intervals. Seed Science Research 20, 123–136.CrossRefGoogle Scholar
Montesinos-López, O.A., Montesinos-López, A., Crossa, J., Eskridge, K. and Sáenz-Casas, R.A. (2011) Optimal sample size for estimating the proportion of transgenic plants using the Dorfman model with a random confidence interval. Seed Science Research 21, 235–246.CrossRefGoogle Scholar
Montesinos-López, O.A., Montesinos-López, A., Crossa, J. and Eskridge, K. (2012) Sample size under inverse negative binomial group testing for accuracy in parameter estimation. PLoS ONE 7, e32250.CrossRefGoogle ScholarPubMed
Newcombe, R.G. (1998) Two-sided CIs for the single proportion: comparison of seven methods. Statistics in Medicine 17, 857–872.3.0.CO;2-E>CrossRefGoogle Scholar
Ortiz-García, S., Ezcurra, E., Schoel, B., Acevedo, F., Soberón, J. and Snow, A.A. (2005) Correction. Proceedings of the National Academy of Sciences, USA 102, 18242.Google Scholar
Pan, Z. and Kupper, L. (1999) Sample size determination for multiple comparison studies treating confidence interval width as random. Statistics in Medicine 18, 1475–1488.3.0.CO;2-0>CrossRefGoogle ScholarPubMed
Peck, C. (2006) Going after BVD. Beef 42, 34–44.Google Scholar
Piñeyro-Nelson, A., Van Heerwaarden, J., Perales, H.R., Serratos-Hernández, J.A., Rangel, A., Hufford, M.B., Gepts, P., Garay-Arroyo, A., Rivera-Bustamante, R. and Álvarez-Buylla, E.R. (2009) Transgenes in Mexican maize: molecular evidence and methodological considerations for GMO detection in landrace populations. Molecular Ecology 18, 750–761.CrossRefGoogle ScholarPubMed
Pritchard, N. and Tebbs, J. (2010) Estimating disease prevalence using inverse binomial pooled testing. Journal of Agricultural, Biological, and Environmental Statistics 16, 70–87.CrossRefGoogle Scholar
Pritchard, N. and Tebbs, J. (2011) Bayesian inference for disease prevalence using negative binomial group testing. Biometrical Journal 53, 40–56.CrossRefGoogle ScholarPubMed
Quist, D. and Chapela, I.H. (2001) Transgenic DNA introgressed into traditional maize landraces in Oaxaca, Mexico. Nature 414, 541–543.CrossRefGoogle ScholarPubMed
Quist, D. and Chapela, I.H. (2002) Quist and Chapela reply. Nature 416, 602.CrossRefGoogle Scholar
R Development Core Team (2013) R: A language and environment for statistical computing [computer software and manual], R Foundation for Statistical Computing. Available athttp://www.r-project.org (accessed accessed 13 June 2013).Google Scholar
Remlinger, K., Hughes-Oliver, J., Young, S. and Lam, R. (2006) Statistical design of pools using optimal coverage and minimal collision. Technometrics 48, 133–143.CrossRefGoogle Scholar
Romanow, L.R., Moyer, J.W. and Kennedy, G.G. (1986) Alteration of efficiencies of acquisition and inoculation of watermelon mosaic virus 2 by plant resistance to the virus and to an aphid vector. Phytopathology 76, 1276–1281.CrossRefGoogle Scholar
Swallow, W.H. (1985) Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology 75, 882–889.CrossRefGoogle Scholar
Tebbs, J.M. and Bilder, C.R. (2004) Confidence intervals procedures for probability of disease transmission in Multiple-Vector-Transfer designs. Journal of Agricultural, Biological and Environmental Statistics 9, 79–90.CrossRefGoogle Scholar
Thompson, K.H. (1962) Estimation of the proportion of vectors in a natural population of insects. Biometrics 18, 568–578.CrossRefGoogle Scholar
Verstraeten, T., Farah, B., Duchateau, L. and Matu, R. (1998) Pooling sera to reduce the cost of HIV surveillance: a feasibility study in a rural Kenyan district. Tropical Medicine and International Health 3, 747–750.CrossRefGoogle Scholar
Watson, M.A. (1936) Factors affecting the amount of infection obtained by aphid transmission of the virus Hy. III. Philosophical Transactions of the Royal Society of London, Series B 226, 457–489.Google Scholar
Yamamura, K. and Hino, A. (2007) Estimation of the proportion of defective units by using group testing under the existence of a threshold of detection. Communications in Statistics – Simulation and Computation 36, 949–957.CrossRefGoogle Scholar