Two-sample rank tests for detecting changes that occur in a small proportion of the treated population

In the course of studying a biological phenomenon thought to be a precursor to chromosome breakage, researchers have found that treatments sometimes produce a higher proportion of "outliers" than do controls. Our examples pertain to smokers and patients undergoing chemotherapy, although the statistical methods developed here would apply to subjects exposed to any other health hazard. We formulate the problem in a nonparametric setting. Locally most powerful rank tests are obtained for mixture alternatives. In one instance, the approximate scores test has the simple form of counting the number of treatment responses above a combined sample percentile. Our test statistics are compared to the Wilcoxon and normal scores tests using empirical power studies and asymptotic efficiencies.