Pairwise comparisons for proportions estimated by pooled testing

When estimating the prevalence of a rare trait, pooled testing can confer substantial benefits when compared to individual testing. In addition to screening experiments for infectious diseases in humans, pooled testing has also been exploited in other applications such as drug testing, epidemiological studies involving animal disease, plant disease assessment, and screening for rare genetic mutations. Within a pooled-testing context, we consider situations wherein different strata or treatments are to be compared with the goals of assessing significant and practical differences between strata and ranking strata in terms of prevalence. To achieve these goals, we first present two simultaneous pairwise interval estimation procedures for use with pooled data. Our procedures rely on asymptotic results, so we investigate small-sample behavior and compare the two procedures in terms of simultaneous coverage probability and mean interval length. We then present a unified approach to determine pool sizes which deliver desired coverage properties while taking testing costs and interval precision into account. We illustrate our methods using data from an observational HIV study involving heterosexual males who use intravenous drugs.