A non-inferiority test of areas under two parametric ROC curves

Equivalence or non-inferiority in diagnostic accuracy of two medical diagnostic tests is a common medical problem. Statistical tests of non-inferiority of diagnostic tests have long been a subject of interest in medicine and biostatistical research. Accuracy of a continuous diagnostic test can be evaluated by the area under a receiver operating characteristic (ROC) curve. A conventional non-inferiority test for areas of two parametric ROC curves has been proposed by Zhou, Obuchowski, and McClish [Zhou XH, Obuchowski NA, McClish DK. Statistical Methods in Diagnostic Medicine. New York: John Wiley; 2002]. In this paper, we showed that this conventional approach is anti-conservative and proposed a new statistical test based on restricted maximum likelihood estimator to achieve designed type I error rate. Simulation studies supported this new test to be appropriate for small sample size or highly correlated diagnostic modalities.