X G Zhao1, W Dai, Y Li, L Tian. 1. Department of Bone and Joint Surgery, The First Affiliated Hospital of Xi'an Medical University, Xi'an 710077, Shaanxi Province, PR China.
Abstract
MOTIVATION: The area under the receiver operating characteristic (ROC) curve (AUC), long regarded as a 'golden' measure for the predictiveness of a continuous score, has propelled the need to develop AUC-based predictors. However, the AUC-based ensemble methods are rather scant, largely due to the fact that the associated objective function is neither continuous nor concave. Indeed, there is no reliable numerical algorithm identifying optimal combination of a set of biomarkers to maximize the AUC, especially when the number of biomarkers is large. RESULTS: We have proposed a novel AUC-based statistical ensemble methods for combining multiple biomarkers to differentiate a binary response of interest. Specifically, we propose to replace the non-continuous and non-convex AUC objective function by a convex surrogate loss function, whose minimizer can be efficiently identified. With the established framework, the lasso and other regularization techniques enable feature selections. Extensive simulations have demonstrated the superiority of the new methods to the existing methods. The proposal has been applied to a gene expression dataset to construct gene expression scores to differentiate elderly women with low bone mineral density (BMD) and those with normal BMD. The AUCs of the resulting scores in the independent test dataset has been satisfactory. CONCLUSION: Aiming for directly maximizing AUC, the proposed AUC-based ensemble method provides an efficient means of generating a stable combination of multiple biomarkers, which is especially useful under the high-dimensional settings. CONTACT: lutian@stanford.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
MOTIVATION: The area under the receiver operating characteristic (ROC) curve (AUC), long regarded as a 'golden' measure for the predictiveness of a continuous score, has propelled the need to develop AUC-based predictors. However, the AUC-based ensemble methods are rather scant, largely due to the fact that the associated objective function is neither continuous nor concave. Indeed, there is no reliable numerical algorithm identifying optimal combination of a set of biomarkers to maximize the AUC, especially when the number of biomarkers is large. RESULTS: We have proposed a novel AUC-based statistical ensemble methods for combining multiple biomarkers to differentiate a binary response of interest. Specifically, we propose to replace the non-continuous and non-convex AUC objective function by a convex surrogate loss function, whose minimizer can be efficiently identified. With the established framework, the lasso and other regularization techniques enable feature selections. Extensive simulations have demonstrated the superiority of the new methods to the existing methods. The proposal has been applied to a gene expression dataset to construct gene expression scores to differentiate elderly women with low bone mineral density (BMD) and those with normal BMD. The AUCs of the resulting scores in the independent test dataset has been satisfactory. CONCLUSION: Aiming for directly maximizing AUC, the proposed AUC-based ensemble method provides an efficient means of generating a stable combination of multiple biomarkers, which is especially useful under the high-dimensional settings. CONTACT: lutian@stanford.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
Authors: Sjur Reppe; Hilde Refvem; Vigdis T Gautvik; Ole K Olstad; Per I Høvring; Finn P Reinholt; Marit Holden; Arnoldo Frigessi; Rune Jemtland; Kaare M Gautvik Journal: Bone Date: 2009-11-14 Impact factor: 4.398