Models for sequentially selecting between two and three experiments for optimal estimation of prevalence rate with imperfect tests

Abstract

The idea of pool testing originated from Dorfman during the World War II as an economical method of testing blood samples of army inductees in order to detect the presence of infection. Dorfman proposed that rather than testing each blood sample individually, portions of each of the samples can be pooled and the pooled sample tested first. If the pooled sample is free of infection, all inductees in the pooled sample are passed with no further tests otherwise the remaining portions of each of the blood samples are tested individually. Apart from classification problem, pool testing can also be used in estimating the prevalence rate of a trait in a population which was the focus of our study. In approximating the prevalence rate, one-at-a-time testing is time consuming, non-cost effective and is bound to errors hence pool testing procedures have been proposed to address these problems. Despite these procedures, when pool testing strategies are used using imperfect kits, there tend to be loss of sensitivity. Lost sensitivity of a test is recovered by retesting pools classified positive in the initial test. This study has developed statistical models which are used to sequentially select some combination of two or three experiments when the sensitivity and specificity of the test kits is less than 100%. The experiments are selected sequentially at each stage so that the information obtained at a given stage is used to determine the experiment to be carried out in the subsequent stage. To accomplish this, the study has employed the method of maximum likelihood estimation in obtaining the estimators. The Fisher information of different experiments is compared and the cut off values where both experiments have the same Fisher information is calculated. The joint experiment models while choosing between two experiments and joint experiment model while choosing between three experiments obtained in this study are found to be more superior to the existing one–at-a-time, pooled and pooled with retesting experiments. Furthermore, asymptotic relative efficiency (ARE) of the joint two and three experiment models are computed and the joint three experiment model found to perform better.