Hypergeometric and binomial group sampling with an imperfect test

Abstract

Group sampling, also known as pooled or batch sampling, is a standard technique implemented in biological sciences and the health sector. Common objectives include the detection of pest species in specific locations, or to infer the prevalence of disease in communities, livestock or wildlife. The purpose of this paper is to support the design of robust group sampling strategies when testing processes are imperfect. We formulate analytical distributions and statistics for grouped-hypergeometric sampling, and its binomial approximation, which incorporate sensitivity and specificity in a variety of ways to suit a wide range of applications. These include tests that respond to the presence or absence of contaminated material in a group, as well as PCR and serological testing processes that respond in distinct ways to the number of contaminated items in each group. Hellinger information is also formulated, which contributes to group-sampling design strategies that increase the accuracy of inferred prevalence from collected data—an essential component in decision-making during outbreaks of disease and in operational biosecurity applications. We use an application of disease monitoring in livestock to demonstrate how results can be used to improve public health. Show more