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Sample size under inverse negative binomial group testing for accuracy in parameter estimation.

Osval Antonio Montesinos-López1, Abelardo Montesinos-López, José Crossa

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This study introduces new sample size methods for estimating genetically modified plant prevalence using group testing. The computational Wald procedure offers the most precise sample size estimations for rare events.

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Area of Science:

  • Agricultural Science
  • Biotechnology
  • Statistical Methods

Background:

  • Group testing is efficient for detecting adventitious presence (AP) of genetically modified plants when prevalence is low.
  • Traditional binomial models are used for estimation and sample size calculations in group testing.
  • Inverse (negative) binomial sampling is preferred for rare events (<0.1 prevalence) in sequential testing.

Purpose of the Study:

  • To propose and evaluate three sample size procedures for estimating AP prevalence using group testing under inverse (negative) binomial sampling.
  • To provide methods for determining the number of positive pools required for accurate prevalence estimation.
  • To assess the precision and assurance of the proposed sample size methods.

Main Methods:

  • Developed two computational and one analytic sample size procedures for inverse (negative) binomial group testing.
  • Utilized the Dorfman model for prevalence estimation with inverse (negative) binomial sampling.
  • Employed Monte Carlo simulations to evaluate coverage and assurance levels of proposed sample sizes.

Main Results:

  • Three sample size procedures were proposed for estimating AP prevalence.
  • The computational Wald procedure (method 2) demonstrated high precision with coverage and assurance levels close to nominal values.
  • The Clopper-Pearson CI based method (method 1) was conservative, overestimating sample size, while the analytic Wald method (method 3) sometimes underestimated it.

Conclusions:

  • The proposed methods ensure precise estimation of AP proportion by controlling confidence interval width.
  • The computational Wald procedure is recommended for its accuracy in determining sample sizes for rare event group testing.
  • Accurate sample size determination is crucial for reliable prevalence estimation in genetically modified plant detection.