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

Abstract

AbstractDetecting 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 ofp. 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 ofpunder 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 (\overline{w}) is narrower than the desired width (ω); and (2) iteratively increase the sample size until\overline{w}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.