A goodness-of-fit test for a receiver operating characteristic curve from continuous diagnostic test data

The receiver operating characteristic (ROC) curve is a useful way to display the performance of a medical diagnostic test for detecting whether or not a patient is diseased or healthy. The diagnostic data consist of independent random samples on continuous measurement scales from diseased and healthy populations. We propose assessing the goodness-of-fit of a model by comparing a model-based estimate with a nonparametric estimate of the area under the curve (AUC). We focus on two parametric models, so-called Bi-Normal and Bi-Weibull models, and briefly on associated semiparametric transformation models. We also consider the null hypothesis that a parametric model is valid after an unspecified monotone transformation of the measurement scales. High power of the test implies sensitivity of the AUC to model assumptions; low power implies robustness of the estimate. The test is exemplified with a data set on the diagnosis of pancreatic cancer. A simulation study of the statistical power of the test is included. (January 2003)