Estimating a Proportion Based on Group Testing for Correlated Binary Response

Journal of Biometrics & Biostatistics

article

Osval A Montesinos-López¹  Abelardo Montesinos-López³  Kent Eskridge²  José Crossa⁴ 

[1] Faculty of Telematics, University of Colima, 333 University Avenue;University of Nebraska, Statistics Department, Lincoln;Department of Statistics, Center for Mathematical Research;Biometrics and Statistics Unit, International Maize and Wheat Improvement Center

关键词: Pools;    Correlated data;    Clusters;    Group testing;    Betabinomial model;   

DOI  :  10.4172/2155-6180.1000185

来源: Hilaris Publisher

【 摘 要 】

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.

【 授权许可】

Unknown