Nonparametric analysis of clustered data in diagnostic trials: Estimation problems in small sample sizes

In diagnostic trials, clustered data are obtained when several subunits (e.g., organs or vessels) of the same patient are observed where no, several, or all subunits may be diseased or non-diseased as classified by a gold standard. In such a design, repeated measures appear in a natural way since the same patient is observed under different conditions by several readers and the repeated measures may have a quite involved correlation structure. A nonparametric method for clustered data in multiple reader studies to estimate the area under the ROC curve has been previously considered. The disadvantage of this procedure is that the test statistic (a quadratic form) can become negative in case of small samples. Therefore, a slightly different approach by weighting the estimators of the areas under the curves (AUC) is proposed. It is shown that the proposed new estimator of the covariance matrix of the weighted AUC estimators is always positive semidefinite. Simulation studies show that the new statistic maintains the pre-assigned type-I error level quite well even in case of small sample sizes. The method is motivated by a real data example where the previously suggested statistic becomes negative. This example demonstrates the advantage of the new method.