Robust and flexible inference for the covariate-specific receiver operating characteristic curve

Diagnostic tests are of critical importance in health care and medical research. Motivated by the impact that atypical and outlying test outcomes might have on the assessment of the discriminatory ability of a diagnostic test, we develop a robust and flexible model for conducting inference about the covariate-specific receiver operating characteristic (ROC) curve that safeguards against outlying test results while also accommodating for possible nonlinear effects of the covariates. Specifically, we postulate a location-scale regression model for the test outcomes in both the diseased and nondiseased populations, combining additive regression B-splines and M-estimation for the regression function, while the distribution of the error term is estimated via a weighted empirical distribution function of the standardized residuals. The results of the simulation study show that our approach successfully recovers the true covariate-specific area under the ROC curve on a variety of conceivable test outcomes contamination scenarios. Our method is applied to a dataset derived from a prostate cancer study where we seek to assess the ability of the Prostate Health Index to discriminate between men with and without Gleason 7 or above prostate cancer, and if and how such discriminatory capacity changes with age.