Research Article

Sample size for detecting and estimating the proportion of transgenic plants with narrow confidence intervals

Osval Antonio Montesinos López^a1, Abelardo Montesinos López^a3, José Crossa^a4 c1, Kent Eskridge^a5 and Carlos Moises Hernández Suárez^a2

^a1 Facultad de Telemática, Universidad de Colima, Bernal Díaz del Castillo No. 340 Col. Villa de San Sebastián, C.P. 28045 Colima, Colima, México

^a2 Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo No. 340 Col. Villa de San Sebastián, C.P. 28045 Colima, Colima, México

^a3 Departamento de Estadística. División de Ciencias Forestales, Universidad Autónoma Chapingo, Texcoco, Estado de México, México

^a4 Biometrics and Statistics Unit of the Crop Research Informatics Laboratory (CRIL) of the Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, México DF, México

^a5 Department of Statistics, University of Nebraska, Lincoln, Nebraska, USA

Abstract

Detecting the presence of genetically modified plants (adventitious presence of unwanted transgenic plants, AP) from outcrossing species such as maize requires a method that lowers laboratory costs without losing precision. Group testing is a procedure in which groups that contain several units (plants) are analysed without having to inspect individual plants, with the purpose of estimating the prevalence of AP in a population at a low cost without losing precision. When pool (group) testing is used to estimate the prevalence of AP (p), there are sampling procedures for calculating a confidence interval (CI); however, they usually do not ensure precision in the estimation of p. This research proposes a method to determine the number of pools (g), given a pool size (k), that ensures precision in the estimated proportion of AP (that is, it ensures a narrow CI). In addition, the study computes the maximum likelihood estimator of p under pool testing and its exact CI, considering the detection limit of the laboratory, d, and the concentration of AP per unit (c). The proposed sample procedure involves two steps: (1) obtain a sample size that guarantees that the mean width of the CI () is narrower than the desired width (ω); and (2) iteratively increase the sample size until is smaller than the desired width (ω) with a specified degree of certainty (γ). Simulated data were created and tables are presented showing the different possible scenarios that a researcher may encounter. An R program is given and explained that will reproduce the results and make it easy for the researcher to create other scenarios.

(Received September 30 2009)

(Accepted January 19 2010)

(Online publication March 03 2010)

Keywords

• adventitious presence of transgenic plants;
• confidence interval;
• confidence interval width;
• pool sampling

Correspondence:

^c1 Correspondence Email: j.crossa@cgiar.org