Efficient estimation of the prevalence of multiple rare traits

We consider a population with multiple traits of interest, where our goal is to estimate the proportions of individuals with the traits. When traits are rare, group testing can improve efficiency. Previous work of Hughes-Oliver & Swallow (1994) developed an adaptive two-stage design for group testing 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 consistent and asymptotically normal. We apply our design to a problem of estimating the prevalence of HIV, chlamydia and syphilis in Ethiopian women.