A wild bootstrap approach for the selection of biomarkers in early diagnostic trials

In early diagnostic trials, particularly in biomarker studies, the aim is often to select diagnostic tests among several methods. In case of metric, discrete, or even ordered categorical data, the area under the receiver operating characteristic (ROC) curve (denoted by AUC) is an appropriate overall accuracy measure for the selection, because the AUC is independent of cut-off points.

For selection of biomarkers the individual AUC's are compared with a pre-defined threshold. To keep the overall coverage probability or the multiple type-I error rate, simultaneous confidence intervals and multiple contrast tests are considered. We propose a purely nonparametric approach for the estimation of the AUC's with the corresponding confidence intervals and statistical tests. This approach uses the correlation among the statistics to account for multiplicity. For small sample sizes, a Wild-Bootstrap approach is presented. It is shown that the corresponding intervals and tests are asymptotically exact.

Extensive simulation studies indicate that the derived Wild-Bootstrap approach keeps and exploits the nominal type-I error at best, even for high accuracies and in case of small samples sizes. The strength of the correlation, the type of covariance structure, a skewed distribution, and also a moderate imbalanced case-control ratio do not have any impact on the behavior of the approach. A real data set illustrates the application of the proposed methods.

We recommend the new Wild Bootstrap approach for the selection of biomarkers in early diagnostic trials, especially for high accuracies and small samples sizes.