Fórmula para estimar la proporción de plantas genéticamente modificadas mediante pruebas de grupo

Abstract

Detection of the presence of genetically modified (accidental presence of unwanted transgenic plants) plants is attracting a great deal of public attention due to food safety concerns. Group testing under the Dorfman models is useful for estimating small proportions (≤ 10 %) because it produces savings of up to 80 % in the required number of diagnostic tests. We propose a sample size formula that guarantees narrow confidence intervals for estimating the proportion, because a high probability ensures that the observed confidence interval (CI) will be less than the specified value. The proposed sample sizes formula is derived by assuming homogeneity in the distribution of transgenic plants in the population and considering an imperfect diagnostic test (sensitivity and specificity less than 1, or less than 100 %). This formula gives the necessary number of groups to estimate the proportion of transgenic plants and guarantees a high probability that the observed CI will be smaller than the desired value. Tables with practical scenarios for researchers are presented here, as well as an R program for obtaining the required sample size in an easy way.