Joint inference about the AUC and Youden index for paired biomarkers

It is common to compare biomarkers' diagnostic or prognostic performance using some summary ROC measures such as the area under the ROC curve (AUC) or the Youden index. We propose to compare two paired biomarkers using both the AUC and the Youden index since the two indices describe different aspects of the ROC curve. This comparison can be made by estimating the joint confidence region (an elliptical area) of the differences of the paired AUCs and the Youden indices. Furthermore, for deciding if one marker is better than the other in terms of both the AUC and the Youden index (J), we can test H0:AUCa≤AUCb or Ja≤Jb against Ha:AUCa>AUCb and Ja>Jb using the paired differences. The construction of such a joint hypothesis is an example of the multivariate order-restricted hypotheses. For such a hypothesis, we propose and compare three testing procedures: (1) the intersection-union test ( IUT ); (2) the conditional test; and (3) the joint test. The performance of the proposed inference methods was evaluated and compared through simulations. The simulation results demonstrate that the proposed joint confidence region maintains the desired confidence level, and all three tests maintain the type I error under the null. Furthermore, among the three proposed testing methods, the conditional test is the preferred approach with markedly larger power consistently than the other two competing methods.