JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1218 10.6339/26-JDS1218 Statistical Data Science VAROC: Value Added Receiver Operating Characteristics Curve BristerDanielle1 https://orcid.org/0000-0001-9125-9277 ChungYunroyunro.chung@asu.edu23∗ College of Liberal Arts and Sciences, Arizona State University, U.S.A. College of Health Solutions, Arizona State University, U.S.A. Virginia G. Piper Center for Personalized Diagnostics, Biodesign Institute, Arizona State University, U.S.A. Corresponding author. Email: yunro.chung@asu.edu. 2026301202600118 Supplementary Material

The R code and data used in Section 5 are available at the Supplementary Material of this paper.

6120251512026 2026 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2026 Open access article under the CC BY license.

The receiver operating characteristics (ROC) curve has been widely used to evaluate the discrimination performance of biomarkers, but it has been criticized for overlooking their underlying distributions. In this paper, we propose a continuous version of the ROC curve that can assess not only the discrimination performance of biomarkers but also their continuity performance. Our method summarizes the biomarker values as conditional tail expectations at varying thresholds and compare them with true positive and false positive rates. The proposed method is particularly useful for an early phase of biomarker study that enrolls heterogeneous disease populations. Analysis of data from an ovarian cancer biomarker study illustrates the practical utility of the proposed method over the standard ROC curve analysis. The proposed methods are implemented in the R package varoc.

 area under the ROC curve biomarker classification outlier sum statistics truncated mean analysis References Bangdiwala SI, Haedo AS, Natal ML, Villaveces A (2008). The agreement chart as an alternative to the receiver-operating characteristic curve for diagnostic tests. Journal of Clinical Epidemiology, 61(9): 866–874. https://doi.org/10.1016/j.jclinepi.2008.04.002 Benjamini Y, Hochberg Y (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 57(1): 289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x Bickel PJ (1965). On some robust estimates of location. The Annals of Mathematical Statistics, 36(3): 847–858. https://doi.org/10.1214/aoms/1177700058 Chen LA, Chen DT, Chan W (2010). The distribution-based p-value for the outlier sum in differential gene expression analysis. Biometrika, 97(1): 246–253. https://doi.org/10.1093/biomet/asp075 Chung Y (2025). varoc. R package version 1.0.0. Efron B (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1): 1–26. https://doi.org/10.1214/aos/1176344552 Feng Z, Pepe MS (2020). Adding rigor to biomarker evaluations—EDRN experience. Cancer Epidemiology, Biomarkers & Prevention, 29(12): 2575–2582. https://doi.org/10.1158/1055-9965.EPI-20-0240 Gönen M (2013). Mixtures of receiver operating characteristic curves. Academic Radiology, 20(7): 831–837. https://doi.org/10.1016/j.acra.2013.03.003 Huang Y, Sullivan Pepe M, Feng Z (2007). Evaluating the predictiveness of a continuous marker. Biometrics, 63(4): 1181–1188. https://doi.org/10.1111/j.1541-0420.2007.00814.x Huber PJ (1972). The 1972 Wald lecture robust statistics: A review. The Annals of Mathematical Statistics, 43(4): 1041–1067. https://doi.org/10.1214/aoms/1177692459 Lee WC (1999). Probabilistic analysis of global performances of diagnostic tests: Interpreting the Lorenz curve-based summary measures. Statistics in Medicine, 18(4): 455–471. https://doi.org/10.1002/(SICI)1097-0258(19990228)18:4<455::AID-SIM44>3.0.CO;2-A Lee WC, Hsiao CK (1996). Alternative summary indices for the receiver operating characteristic curve. Epidemiology, 7(6): 605–611. https://doi.org/10.1097/00001648-199611000-00007 López-Ratón M, Rodríguez-Álvarez MX, Cadarso-Suárez C, Gude-Sampedro F (2014). Optimalcutpoints: An R package for selecting optimal cutpoints in diagnostic tests. Journal of Statistical Software, 61: 1–36. https://doi.org/10.18637/jss.v061.i08 Lorenz MO (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70): 209–219. https://doi.org/10.1080/15225437.1905.10503443 Martínez-Camblor P, Corral N, Rey C, Pascual J, Cernuda-Morollón E (2017). Receiver operating characteristic curve generalization for non-monotone relationships. Statistical Methods in Medical Research, 26(1): 113–123. https://doi.org/10.1177/0962280214541095 Martínez-Camblor P, Pardo-Fernández JC (2019). Parametric estimates for the receiver operating characteristic curve generalization for non-monotone relationships. Statistical Methods in Medical Research, 28(7): 2032–2048. https://doi.org/10.1177/0962280217747009 Martínez-Camblor P, Pérez-Fernández S, Díaz-Coto S (2019). Improving the biomarker diagnostic capacity via functional transformations. Journal of Applied Statistics, 46(9): 1550–1566. https://doi.org/10.1080/02664763.2018.1554628 Parmigiani G (2019). The fuzzy ROC. arXiv preprint: https://arxiv.org/abs/1903.01868v1 Pepe MS (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press, Oxford. Pepe MS, Etzioni R, Feng Z, Potter JD, Thompson ML, Thornquist M, et al. (2001). Phases of biomarker development for early detection of cancer. Journal of the National Cancer Institute, 93(14): 1054–1061. https://doi.org/10.1093/jnci/93.14.1054 Pepe MS, Feng Z, Huang Y, Longton G, Prentice R, Thompson IM, et al. (2008a). Integrating the predictiveness of a marker with its performance as a classifier. American Journal of Epidemiology, 167(3): 362–368. https://doi.org/10.1093/aje/kwm305 Pepe MS, Feng Z, Janes H, Bossuyt PM, Potter JD (2008b). Pivotal evaluation of the accuracy of a biomarker used for classification or prediction: Standards for study design. Journal of the National Cancer Institute, 100(20): 1432–1438. https://doi.org/10.1093/jnci/djn326 Pepe MS, Longton G, Anderson GL, Schummer M (2003). Selecting differentially expressed genes from microarray experiments. Biometrics, 59(1): 133–142. https://doi.org/10.1111/1541-0420.00016 Schummer M, Ng WV, Bumgarner RE, Nelson PS, Schummer B, Bednarski DW, et al. (1999). Comparative hybridization of an array of 21500 ovarian cdnas for the discovery of genes overexpressed in ovarian carcinomas. Gene, 238(2): 375–385. https://doi.org/10.1016/S0378-1119(99)00342-X Stigler SM (1973). The asymptotic distribution of the trimmed mean. The Annals of Statistics, 1(3): 472–477. https://doi.org/10.1214/aos/1176342412 Tibshirani R, Hastie T (2007). Outlier sums for differential gene expression analysis. Biostatistics, 8(1): 2–8. https://doi.org/10.1093/biostatistics/kxl005 Tukey JW, McLaughlin DH (1963). Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/winsorization 1. Sankhya. Series A, 25(3): 331–352. Vickers AJ, Elkin EB (2006). Decision curve analysis: A novel method for evaluating prediction models. Medical Decision Making, 26(6): 565–574. https://doi.org/10.1177/0272989X06295361 Wu B (2007). Cancer outlier differential gene expression detection. Biostatistics, 8(3): 566–575. https://doi.org/10.1093/biostatistics/kxl029 Yang J, Kuan PF, Li X, Li J, Zhou XH (2024). Transformed ROC curve for biomarker evaluation. Statistics in Medicine, 43(30): 5681–5697. https://doi.org/10.1002/sim.10268 Youden WJ (1950). Index for rating diagnostic tests. Cancer, 3(1): 32–35. https://doi.org/10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3 Yuen KK (1974). The two-sample trimmed t for unequal population variances. Biometrika, 61(1): 165–170. https://doi.org/10.1093/biomet/61.1.165 Yuen KK, Dixon W (1973). The approximate behaviour and performance of the two-sample trimmed t. Biometrika, 60(2): 369–374. https://doi.org/10.1093/biomet/60.2.369