A network approach to compute hypervolume under receiver operating characteristic manifold for multi-class biomarkers

Computation of hypervolume under ROC manifold (HUM) is necessary to evaluate biomarkers for their capability to discriminate among multiple disease types or diagnostic groups. However the original definition of HUM involves multiple integration and thus a medical investigation for multi-class receiver operating characteristic (ROC) analysis could suffer from huge computational cost when the formula is implemented naively. We introduce a novel graph-based approach to compute HUM efficiently in this article. The computational method avoids the time-consuming multiple summation when sample size or the number of categories is large. We conduct extensive simulation studies to demonstrate the improvement of our method over existing R packages. We apply our method to two real biomedical data sets to illustrate its application.