Receiver Operating Characteristic Curves and Confidence Bands for Support Vector Machines

TL;DR

This paper introduces a method for constructing confidence bands for ROC curves estimated by weighted SVMs, demonstrating their theoretical validity and superior diagnostic performance in biomedical applications.

Contribution

It develops a theoretical framework for confidence bands of SVM ROC curves and shows their practical advantages over existing methods in biomedical diagnostics.

Findings

Confidence bands for SVM ROC curves are theoretically justified.

Weighted SVMs outperform traditional methods in sensitivity and specificity.

Demonstrated effectiveness in hepatitis C diagnosis and breast cancer treatment response prediction.

Abstract

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.