Abstract
BackgroundThe group testing method has been proposed for the detection and estimation of genetically modified plants (adventitious presence of unwanted transgenic plants, AP). For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. However, when the event is rare (low prevalence <0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred.Methodology/Principal FindingsThis research proposes three sample size procedures (two computational and one analytic) for estimating prevalence using group testing under inverse (negative) binomial sampling. These methods provide the required number of positive pools (), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model and inverse (negative) binomial sampling. We give real and simulated examples to show how to apply these methods and the proposed sample-size formula. The Monte Carlo method was used to study the coverage and level of assurance achieved by the proposed sample sizes. An R program to create other scenarios is given in Appendix S2.ConclusionsThe three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width (), with a probability of . With the Monte Carlo study we found that the computational Wald procedure (method 2) produces the more precise sample size (with coverage and assurance levels very close to nominal values) and that the samples size based on the Clopper-Pearson CI (method 1) is conservative (overestimates the sample size); the analytic Wald sample size method we developed (method 3) sometimes underestimated the optimum number of pools.
Highlights
To detect the presence of a rare event, thousands of individuals need to be tested, and the cost of such testing usually exceeds the available budget and staff
The three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width (v), with a probability of c
With the Monte Carlo study we found that the computational Wald procedure produces the more precise sample size and that the samples size based on the Clopper-Pearson CI is conservative; the analytic Wald sample size method we developed sometimes underestimated the optimum number of pools
Summary
To detect the presence of a rare event, thousands of individuals need to be tested, and the cost of such testing usually exceeds the available budget and staff. The pooling methodology (Dorfman method) was first proposed to save a significant amount of money when detecting soldiers with syphilis [1]. Most applications for detecting and estimating a proportion are developed using binomial sampling; Pritchard and Tebbs [9] have suggested that inverse (negative) binomial pooled sampling may be preferred when prevalence p is known to be small, when sampling and testing occur sequentially, or when positive pool results require immediate analysis—for example, in the case of many rare diseases. For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. When the event is rare (low prevalence ,0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred
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