More powerful likelihood ratio tests for isotonic binomial proportions

Binomial group testing involves pooling individuals into groups and observing a binary response on each group. Results from the group tests can then be used to draw inference about population proportions. Its use as an experimental design has received much attention in recent years, especially in public-health screening experiments and vector-transfer designs in plant pathology. We investigate the benefits of group testing in situations wherein one desires to test whether or not probabilities are increasingly ordered across the levels of an observed qualitative covariate, i.e., across strata of a population or among treatment levels. We use a known likelihood ratio test for individual testing, but extend its use to group-testing situations to show the increases in power conferred by using group testing when operating in this constrained parameter space. We apply our methods to data from an HIV study involving male subjects classified as intraveneous drug users.