Dual screening

We discuss the problem of screening a general population for characteristics such as HIV or drug use. Our main approach is Bayesian, which allows for the incorporation of prior information about parameters. In the particular problem we consider, there is currently no information in the data for estimating the sensitivity of the screening test, and consequently, the prevalence of the characteristic among screened negatives cannot be estimated from the collected data alone. Our inferences are straightforward to obtain using Gibbs sampling techniques, and they are valid for large or small samples and for arbitrary prevalence or accuracy of screening tests. We also develop the maximum-likelihood approach using the EM algorithm.