Receiver Operating Characteristic Curves and Confidence Bands for Support Vector Machines
This work addresses the need for robust, nonparametric ROC curve estimation with confidence bands in biomedical applications, offering incremental improvements in theoretical justification and practical performance over existing methods.
The authors tackled the problem of estimating receiver operating characteristic (ROC) curves for binary classification in biomedical decision-making, proposing a method to construct confidence bands for weighted support vector machines (SVMs) and demonstrating superior sensitivity and specificity compared to common methods in simulations and real-world examples like hepatitis C diagnosis and breast cancer treatment prediction.
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.