Estimating ordered binomial proportions with the use of group testing

This paper considers group testing when the probability of response is increasing across the levels of an observed covariate. We illustrate how previously known results in order-restricted inference can be extended to situations wherein data are collected according to a group-testing protocol, and we derive maximum likelihood estimators for proportions under the increasing order restriction and group-testing model. Finally, we show how the use of group testing can dramatically reduce the bias and mean squared error of isotonic regression estimators obtained from one-at-a-time testing. These proposed methods are illustrated using data from an observational HIV study conducted in Houston, Texas.