Sample size for detecting transgenic plants using inverse binomial group testing with dilution effect

Montesinos‐López, Osval A.; Montesinos‐López, Abelardo; Crossa, J.; Eskridge, Kent M.

doi:10.1017/s0960258513000238

Cited by 5 publications

(2 citation statements)

References 34 publications

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“…Pritchard and Tebbs 7,8 proposed several point and interval estimators. Montesinos-Lopez et al 9,10 proposed using sample size under inverse binomial group testing for accuracy in parameter estimation, and Hepworth 3 suggested methods to improve the estimation of proportions using inverse binomial group testing.…”

Section: Introductionmentioning

confidence: 99%

Inverse sampling regression for pooled data

Montesinos‐López

Eskridge

et al. 2015

Stat Methods Med Res

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Because pools are tested instead of individuals in group testing, this technique is helpful for estimating prevalence in a population or for classifying a large number of individuals into two groups at a low cost. For this reason, group testing is a well-known means of saving costs and producing precise estimates. In this paper, we developed a mixed-effect group testing regression that is useful when the data-collecting process is performed using inverse sampling. This model allows including covariate information at the individual level to incorporate heterogeneity among individuals and identify which covariates are associated with positive individuals. We present an approach to fit this model using maximum likelihood and we performed a simulation study to evaluate the quality of the estimates. Based on the simulation study, we found that the proposed regression method for inverse sampling with group testing produces parameter estimates with low bias when the pre-specified number of positive pools (r) to stop the sampling process is at least 10 and the number of clusters in the sample is also at least 10. We performed an application with real data and we provide an NLMIXED code that researchers can use to implement this method.

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Section: Introductionmentioning

confidence: 99%

Inverse sampling regression for pooled data

Montesinos‐López

Eskridge

et al. 2015

Stat Methods Med Res

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“…The group testing model of Dorfman [1] is effective for reducing the number of diagnostic tests because instead of performing n individual diagnostic tests, it only requires = n g k when retesting is not done (where k is the pool size). However, caution needs to be exercised when choosing the pool size (k), because if k is too large, the diagnostic test may be sensitive to dilution effects [2,3]. Assuming perfect testing, a pool is declared positive if at least one of the k individuals is positive, and declared free of the disease if the test is negative.…”

Section: Introductionmentioning

confidence: 99%

Estimating a Proportion Based on Group Testing for Correlated Binary Response

Montesinos‐López¹,

Montesinos‐López²,

Eskridge³

et al. 2013

J Biom Biostat

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When the sampling scheme is in clusters and when the pools (of size k) within a cluster are assumed not to be independent, the Dorfman model for estimating the proportion under the binomial model is incorrect. The purpose of this paper is to propose a method for analyzing correlated binary data under the group testing framework. First, assuming that the probability of an individual varies according to a beta distribution, we derived an analytic expression for the probability of a positive pool and the correlation between two pools in each cluster. Second, we derived the exact probability mass function of the number of positive pools in each cluster that should be used to obtain the maximum likelihood estimate (MLE) of the proportion of individuals with a positive outcome. However, this MLE is not efficient in terms of computational resources. For this reason, we proposed another estimator based on the beta-binomial model for obtaining the approximate MLE of the proportion of interest. Based on a simulation study, the approximate estimator produced results that are very close to the exact MLE of the proportion of interest, with the advantage that this approach is computationally more efficient.Liu et al. [6] provide confidence interval procedures for estimating proportions estimated by group testing with groups of unequal size adjusted for overdispersion (extra-binomial variation). They used a quasi-likelihood approach to correct for the presence of overdispersion. However, in this case, heterogeneity in pool responses is induced by using different pool sizes (k) and may be due to the number of pools per cluster used in the group testing method. In their study, Liu et al.[6] introduced heterogeneity by assuming three clusters (m=3) and using a different pool size (k 1 ,k 2 ,k 3 ) in each cluster, with the following number of pools per cluster: N 1 =5, N 2 =10 and N 3 =15. For example, when k 1 =20, k 2 =10 and k 3 =5, they observed that if Y 1 =5, Y 2 =7 and 3 =4, then 2 1. 28 00 σ = , where Y i denote the number of positive pools observed, i=1,2,3, and 2 σ denotes the estimated dispersion parameter.However, if Y 1 =1, Y 2 =7 and Y 3 =3, then 2 4. 33 07 σ = , which indicates that the proportion of group testing varies widely for specific combinations; this also implies the presence of overdispersion. Here it is important to point out that the outcomes of the units in each cluster are assumed to be independent, identically distributed (i.i.d.) binomial distributions Table 2: Relative bias (RB) and relative mean squared error (RMSE) for the beta-binomial model and Relative bias (RB E ) for the exact distribution (Eq. 3), using various combinations of π, δ and N with k=25 and n l =10, l=1,2,…,N.Relative bias (RB) for the beta-binomial model (in black) and for the true model (in red) with various combinations of π, Citation: Montesinos-López OA, Montesinos-López A, Eskridge K, Crossa J (2014) Estimating a Proportion Based on Group Testing for Correlated Binary Response. J Biomet Biostat 5: 185.

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Nonparametric and Parametric Estimators of Prevalence From Group Testing Data With Aggregated Covariates

Delaigle

Zhou

2015

Journal of the American Statistical Association

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Group testing is a technique employed in large screening studies involving infectious disease, where individuals in the study are grouped before being observed. Parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature, in the case where the binary variable indicating the disease status is available only for the group, but the explanatory variable is observed for each individual. However, for reasons such as the high cost of assays, the confidentiality of the patients, or the impossibility of measuring a concentration under a detection limit, the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid. We develop consistent parametric and nonparametric estimators of the conditional prevalence in this complex problem. We establish theoretical properties of our estimators and illustrate their practical performance on simulated and real data. We extend our techniques to the case where the group status is measured imperfectly, and to the setting where the covariate is aggregated and the individual status is available.

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Sample size for detecting transgenic plants using inverse binomial group testing with dilution effect

Cited by 5 publications

References 34 publications

Inverse sampling regression for pooled data

Inverse sampling regression for pooled data

Estimating a Proportion Based on Group Testing for Correlated Binary Response

Nonparametric and Parametric Estimators of Prevalence From Group Testing Data With Aggregated Covariates

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