Two-stage negative binomial group testing model for estimating prevalence of a rare trait

Abstract

Group testing is an economical screening strategy that is beneficial in terms of efficiency and cost-cutting. The idea dates back to World War II, and it entails amalgamating individual specimens into pools that are tested for the presence of a trait of interest. Since its inception, group testing literature has branched into two research areas: classification and estimation. Research work in group testing has concentrated on designs without errors and has mainly developed under the binomial model. However, a combination of inverse sampling and group testing has been established to be useful when there is a need to report estimates early in the screening process. The main focus under the negative binomial group testing designs has been to develop more efficient estimators and to determine optimum group sizes under the assumption that the testing process has no misclassification. However, errors associated with labelling, and misclassification are prone to occur in an experimental design. Retesting of pools has been established to improve the efficiency of an estimator and increase the precision of a test. This research has constructed and analyzed a two-stage negative binomial group testing model for estimating the prevalence of a rare trait when imperfect tests with known sensitivity and specificity are used. The study utilized the Maximum Likelihood Estimation (MLE) method to obtain the estimator and the Cramer-Rao bound method to compute the Fischer information of the estimator. The properties of the constructed estimator were examined. The efficiency of the constructed estimator relative to other estimators in pool testing designs was determined by computing the Asymptotic Relative Efficiency (ARE) and the Relative Mean Squared Error (RMSE). The procedure was illustrated, and the model was verified by performing Monte Carlo simulations using R programming language version 3.5.2. The research findings showed that the model was superior to the one-stage negative binomial group testing model with misclassification as low variances were obtained as the proportion p increased. Also, the constructed estimator performed more efficiently for higher values of p. Furthermore, the study can be used for surveillance of pathogens and monitoring the prevalence of infectious diseases such as the Coronavirus disease 2019 (COVID-19) to prevent another pandemic resurgence.