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Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.

ABSTRACT: In biomedical studies, it is often of interest to classify/predict a subject's disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on area under the receiver operating characteristic curve (AUC). Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in suboptimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data are generated from a semiparametric generalized linear model, just as the smoothed AUC method. Through simulation studies and real data examples, we demonstrate that RAUC outperforms smooth AUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. Copyright © 2016 John Wiley & Sons, Ltd.

SUBMITTER: Fong Y

PROVIDER: S-EPMC4965290 | biostudies-literature | 2016 Sep

REPOSITORIES: biostudies-literature

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Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.

Fong Youyi Y Yin Shuxin S Huang Ying Y

Statistics in medicine 20160405 21

In biomedical studies, it is often of interest to classify/predict a subject's disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on area under the receiver operating characteristic curve (AUC). Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perfor ...[more]

PMID: 27058981

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Project description:BACKGROUND: The receiver operating characteristic (ROC) curve is a fundamental tool to assess the discriminant performance for not only a single marker but also a score function combining multiple markers. The area under the ROC curve (AUC) for a score function measures the intrinsic ability for the score function to discriminate between the controls and cases. Recently, the partial AUC (pAUC) has been paid more attention than the AUC, because a suitable range of the false positive rate can be focused according to various clinical situations. However, existing pAUC-based methods only handle a few markers and do not take nonlinear combination of markers into consideration. RESULTS: We have developed a new statistical method that focuses on the pAUC based on a boosting technique. The markers are combined componentially for maximizing the pAUC in the boosting algorithm using natural cubic splines or decision stumps (single-level decision trees), according to the values of markers (continuous or discrete). We show that the resulting score plots are useful for understanding how each marker is associated with the outcome variable. We compare the performance of the proposed boosting method with those of other existing methods, and demonstrate the utility using real data sets. As a result, we have much better discrimination performances in the sense of the pAUC in both simulation studies and real data analysis. CONCLUSIONS: The proposed method addresses how to combine the markers after a pAUC-based filtering procedure in high dimensional setting. Hence, it provides a consistent way of analyzing data based on the pAUC from maker selection to marker combination for discrimination problems. The method can capture not only linear but also nonlinear association between the outcome variable and the markers, about which the nonlinearity is known to be necessary in general for the maximization of the pAUC. The method also puts importance on the accuracy of classification performance as well as interpretability of the association, by offering simple and smooth resultant score plots for each marker.

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Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.

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Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.

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