Determining the infection status of a herd

This article presents hierarchical models for determining infection status and prevalence of infection within a herd given a hypergeometric or binomial sample of animals that have been screened with an imperfect test. Expert prior information on the infection status of the herd, diagnostic test accuracy, and herd prevalence is incorporated into the model. Posterior probabilities versus prior probabilities of infection are presented in the novel form of a curve, summarizing the probability of infection over a range of possible prior probability values. We demonstrate the model with serologic data for Mycobacterium paratuberculosis (Johne's disease) in dairy herds.