Semiparametric Estimation of ROC Curve Under Test-Result-Dependent Sampling

The receiver operating characteristic (ROC) curve may be used to evaluate the performance of a biomarker measured on continuous scale to predict disease status or clinical condition. Motivated by the need for novel study designs with better estimation efficiency and reduced study cost, we consider in this article a biased sampling scheme that consists of a simple random component and a supplemented testresult- dependent component. Using this approach, investigators can oversample or undersample subjects falling into certain ranges of the biomarker score, allowing an improved precision for the estimation of the ROC curve with a fixed size of subjects. Of course, this sampling scheme will introduce bias in the assessment of the predictive accuracy of the biomarker under standard ROC estimation methods. We develop a semiparametric empirical likelihood method to estimate a covariate-specific ROC curve and a marginal ROC curve, where the latter is an average of the covariatespecific ROC curves over the covariate distribution. We establish the asymptotic properties of the proposed estimators and give their corresponding variance estimators. Simulation studies show that the proposed estimation method yields good small sample properties and is more efficient than alternative methods. The proposed method is illustrated with an example based on the design of an ongoing lung cancer clinical trial