Comparison of ROC umbrella volumes with an application to the assessment of lung cancer diagnostic markers

Receiver operating characteristic (ROC) analysis is widely used to assess the ability of diagnostic markers to correctly classify into one of two disease classes. ROC surfaces and umbrella surfaces generalize the utility of ROC analysis when there are three disease classes. Identification of lung cancer diagnostic markers is an active area of research since prognosis for those diagnosed with lung cancer is so poor and there is not an accurate method for early detection of lung cancer. A study conducted for the assessment of DNA methylation markers motivated the comparison of ROC umbrella surfaces which is developed in this article using U-statistics and bootstrap methodology.