Rank methods for the analysis of clustered data in diagnostic trials

Methods for comparing areas under receiver operating characteristic curves usually depend on the assumption of independence between diseased and nondiseased units in the trial. However, if several parts of the same subject have to be classified as diseased or nondiseased, such observations are no longer independent. This situation is referred to as clustered data. First ideas for the analysis of such data are based on the theory of U-statistics. The idea of the multivariate nonparametric Behrens–Fisher problem is extended to clustered data and to factorial designs. ANOVA-type statistics are suggested for both small and moderate sample sizes. They are evaluated in a simulation study and applied to a real-data example.