An Almost Unbiased Estimator in Group Testing with Errors in Inspection

Abstract

The idea of pooling samples into pools as a cost effective method of screening individuals for the presence of a disease in a large population is discussed. Group testing was designed to reduce diagnostic cost. Testing population in pools also lower misclassification errors in low prevalence population. In this study we violate the assumption of homogeneity and perfect tests by investigating estimation problem in the presence of test errors. This is accomplished through Maximum Likelihood Estimation (MLE). The purpose of this study is to determine an analytical procedure for bias reduction in estimating population prevalence using group testing procedure in presence of tests errors. Specifically, we construct an almost unbiased estimator in pool-testing strategy in presence of test errors and compute the modified MLE of the prevalence of the population. For single stage procedures, with equal group sizes, we also propose a numerical method for bias correction which produces an almost unbiased estimator with errors. The existence of bias has been shown with the help of Taylor's expansion series, for group sizes greater than one. The indicator function with errors is used in the development of the model. A modified formula for bias correction has been analytically shown to reduce the bias of a group testing model. Also, the Fisher information and asymptotic variance has been shown to exist. We use MATLAB software for simulation and verification of the model. Then various tables are drawn to illustrate how the modified bias formula behaves for different values of sensitivities and specificities.