Efficient estimation of the prevalence of multiple rare traits

We consider a population with multiple traits of interest, where our goal i s to estimate the proportions of individuals with the traits. When traits a re rare, group testing can improve efficiency. Previous work of Hughes-Oliv er & Swallow (1994) developed an adaptive two-stage design for group testin g of only one trait. We extend this work to the multi-trait case. We derive the optimum group sizes using compound D-optimum design theory. Estimation is based on maximum likelihood estimators, which are shown to be consisten t and asymptotically normal. We apply our design to a problem of estimating the prevalence of HIV, chlamydia and syphilis in Ethiopian women.