Abstract
The covariate-specific receiver operating characteristic (ROC) curve is an important tool for evaluating the classification accuracy of a diagnostic test when it is associated with certain covariates. In this paper, a weighted Wilcoxon estimator is constructed for estimating this curve under the framework of location-scale model for the test result. The asymptotic normality is established, both for the regression parameter estimator and the estimator for the covariate-specific ROC curve at a fixed false positive point. Simulation results show that the Wilcoxon estimator compares favorably to its main competitors in terms of the standard error, especially when outliers exist in the covariates. As an illustration, the new procedure is applied to the dementia data from the national Alzheimer’s coordinating center.
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References
Duan X G, Zhou X H. Composite quantile regression for the receiver operating characteristic curve. Biometrika, 2013, 100: 889–900
Faraggi D. Adjusting receiver operating characteristic curves and related indices for covariates. J Roy Statist Soc Ser D, 2003, 52: 179–192
González-Manteiga W, Pardo-Fernández J C, Van Keilegom I. ROC curves in nonparametric location-scale regression models. Scand J Statist, 2011, 38: 169–184
Heagerty P J, Pepe M S. Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children. Appl Statist, 1999, 48: 533–551
Hettmansperger T P, Mckean J W. Robust Nonparametric Statistical Methods. New York: Wiley, 1998
Knight K. Limiting distributions for l 1 regression estimators under general conditions. Ann Statist, 1998, 26: 755–770
Leng C. Varible selection and coefficient estimation via regularized rank regression. Statist Sinica, 2010, 20: 167–181
Liu D P, Zhou X H. Nonparametric estimation of the covariate-specific ROC curve in presence of ignorable verification bias. Biometrics, 2011, 67: 906–916
Ma S G, Huang J. Regularized ROC method for disease classification and biomarker selection with microarray data. Bioinformatics, 2005, 21: 4356–4362
McKean J W. Robust analysis of linear models. Statist Sci, 2004, 19: 562–570
Pepe M S. A Regression modelling framework for receiver operating characteristic curves in medical diagnostic testing. Biometrika, 1997, 84: 595–608
Pepe M S. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics, 1998, 54: 124–135
Pepe M S. Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford: Oxford University Press, 2003
Sherman R. The limiting distribution of the maximum rank correlation estimator. Econometrica, 1993, 61: 123–137
Sievers G. A weighted dispersion function for estimation in linear models. Comm Statist Theory Methods, 1983, 12: 1161–1179
Terpstra J T, McKean J W. Rank-based analyses of linear models using R. J Statist Softw, 2005, 14: 1–26
Wang L, Li R Z. Weighted wilcoxon-type smoothly clipped absolute deviation method. J Amer Statist Assoc, 2009, 104: 1631–1645
Wang Y J, Chen H H, Li R Z, et al. Prediction-based structured variable selection through the receiver operating characteristic curves. Biometrics, 2011, 67: 896–905
Zheng Y, Heagerty P J. Semiparametric estimation of time-dependent ROC curves for longitudinal marker data. Biostatistics, 2004, 5: 615–632
Zhou X H, Obuchowski N A, McClish D K. Statistical Methods in Diagnostic Medicine, 2nd ed. New York: Wiley, 2011
Zou H, Yuan M. Composite quantile regression and the oracle model selection theory. Ann Statist, 2008, 36: 1108–1126
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11401561 and 11301031). The authors thank two referees for their valuable suggestions, and the National Alzheimer’s Coordinating Center for providing the data for analysis (the interpretation and reporting of the data are the sole responsibility of the authors).
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Zhang, Q., Duan, X. & Zhou, X. A weighted Wilcoxon estimate for the covariate-specific ROC curve. Sci. China Math. 60, 1705–1716 (2017). https://doi.org/10.1007/s11425-015-0158-0
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DOI: https://doi.org/10.1007/s11425-015-0158-0