  Many problems that appear in biomedical decision making, such as diagnosing
disease and predicting response to treatment, can be expressed as binary
classification problems. The costs of false positives and false negatives vary
across application domains and receiver operating characteristic (ROC) curves
provide a visual representation of this trade-off. Nonparametric estimators for
the ROC curve, such as a weighted support vector machine (SVM), are desirable
because they are robust to model misspecification. While weighted SVMs have
great potential for estimating ROC curves, their theoretical properties were
heretofore underdeveloped. We propose a method for constructing confidence
bands for the SVM ROC curve and provide the theoretical justification for the
SVM ROC curve by showing that the risk function of the estimated decision rule
is uniformly consistent across the weight parameter. We demonstrate the
proposed confidence band method and the superior sensitivity and specificity of
the weighted SVM compared to commonly used methods in diagnostic medicine using
simulation studies. We present two illustrative examples: diagnosis of
hepatitis C and a predictive model for treatment response in breast cancer.
