Facultad de Telemática, Universidad de Colima, Colima, Colima, México.
PLoS One. 2012;7(3):e32250. doi: 10.1371/journal.pone.0032250. Epub 2012 Mar 22.
The 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 FINDINGS: This 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 ([Formula: see text]), 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.
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 ([Formula: see text]), with a probability of [Formula: see text]. 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.
群体检测方法已被提议用于检测和估计转基因植物（意外存在不需要的转基因植物，AP）。对于二元响应变量（存在或不存在），当流行率较低时，群体检测是有效的，因此已经在二项式模型下开发了估计、检测和样本量方法。然而，当事件很少见（低流行率<0.1）并且测试是顺序进行时，逆（负）二项式 pooled 采样可能是首选。
方法/主要发现：本研究提出了三种使用逆（负）二项式抽样进行群体检测估计流行率的样本量程序（两种计算和一种分析）。这些方法提供了在 Dorfman 模型和逆（负）二项式抽样下估计 AP 植物比例所需的正池数量（[公式：见正文]）。我们给出了真实和模拟的例子，展示了如何应用这些方法和提出的样本量公式。蒙特卡罗方法用于研究所提出的样本量的覆盖范围和置信水平。附录 S2 中给出了一个用于创建其他场景的 R 程序。
这三种方法确保了估计的 AP 比例的精度，因为它们保证置信区间（CI）的宽度（W）将等于或小于所需的宽度（[公式：见正文]），置信概率为[公式：见正文]。通过蒙特卡罗研究，我们发现计算 Wald 程序（方法 2）产生更精确的样本量（覆盖率和保证水平非常接近标称值），而基于 Clopper-Pearson CI 的样本量（方法 1）是保守的（高估了样本量）；我们开发的分析 Wald 样本量方法（方法 3）有时低估了最优池数。
