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Cumulative/dynamic ROC curve estimation. (English) Zbl 07184816

Summary: Receiver operating-characteristic (ROC) curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous (bio)markers. When the considered outcome is a time-dependent variable, the direct generalization is known as cumulative/dynamic ROC curve. For a fixed point of time, \(t\), one subject is allocated into the positive group if the event happens before \(t\) and into the negative group if the event is not happened at \(t\). The presence of censored subject, which can not be directly assigned into a group, is the main handicap of this approach. The proposed cumulative/dynamic ROC curve estimator assigns a probability to belong to the negative (positive) group to the subjects censored previously to \(t\). The performance of the resulting estimator is studied from Monte Carlo simulations. Some real-world applications are reported. Results suggest that the new estimators provide a good approximation to the real cumulative/dynamic ROC curve.

MSC:

62-XX Statistics
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[1] Green DM, Swets JA. Signal detection theory and psychophysics. New York: Wiley; 1966. [Google Scholar]
[2] Martínez-Camblor P. Area under the ROC curve comparison in the presence of missing data. J Korean Statist Soc. 2013;42(4):431-442. doi: 10.1016/j.jkss.2013.01.004[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1294.62098
[3] Moise A, Clement B, Raissis M. A test for crossing receiver operating characteristic (ROC) curves. Commun Stat -Theory Methods. 1988;17:1985-2003. doi: 10.1080/03610928808829727[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[4] Venkatraman ES, Begg CB. A distribution-free procedure for comparing receiver operating characteristic curves from a paired experiment. Biometrika. 1996;83(4):835-848. doi: 10.1093/biomet/83.4.835[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0883.62046
[5] Venkatraman ES. A permutation test to compare receiver operating characteristic curves. Biometrics. 2000;56:1134-1138. doi: 10.1111/j.0006-341X.2000.01134.x[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1060.62520
[6] Bandos AI, Rockette HE, Gur D. A permutation test sensitive to differences in areas for comparing ROC curves from paired design. Stat Med. 2005;24:2873-2893. doi: 10.1002/sim.2149[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[7] Braun T, Alonzo TA. A modified sign test for comparing paired ROC curves. Biostatistics. 2008;9:364-372. doi: 10.1093/biostatistics/kxm036[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1143.62027
[8] Martínez-Camblor P, Carleos C, Corral N. Powerful nonparametric statistics to compare k-independent ROC curves. J Appl Stat. 2011;38(7):1317-1332. doi: 10.1080/02664763.2010.498504[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1218.62041
[9] Krzanowski WJ, Hand DJ. Testing the difference between two Kolmogorov-Smirnov values in the context of receiver operating characteristic curves. J Appl Stat. 2011;38(3):437-450. doi: 10.1080/02664760903456400[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1511.62348
[10] Martínez-Camblor P, Carleos C, Corral N. General nonparametric ROC curves comparison. J Korean Statist Soc. 2013;42:71-81. doi: 10.1016/j.jkss.2012.05.002[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1294.62099
[11] Cai T. Semi-parametric ROC regression analysis with placement values. Biostatistics. 2004;5(1):45-60. doi: 10.1093/biostatistics/5.1.45[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1096.62112
[12] Rodríguez-Álvarez MX, Tahoces PG, Cadarso-Suárez C, Lado MJ. Comparative study of ROC regression techniques-Applications for the computed-aided diagnostic system in breast cancer detection. Comput Stat Data Anal. 2011;55(1):888-902. doi: 10.1016/j.csda.2010.07.018[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1247.62282
[13] Heagerty P, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics. 2005;61(1):92-105. doi: 10.1111/j.0006-341X.2005.030814.x[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1077.62077
[14] Wolf P, Schmidt G, Ulm K. The use of ROC for defining the validity of the prognostic index in censored data. Stat Probab Lett. 2011;81:783-791. doi: 10.1016/j.spl.2011.02.021[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1218.62104
[15] Rutter CM, Gatsonis CA. A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Stat Med. 2001;20:2865-2884. doi: 10.1002/sim.942[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[16] Martínez-Camblor P. Fully non-parametric ROC curve estimation for random-effects meta-analysis. Statist Methods Med Res. 2014, doi: 10.1177/0962280214537047. [Google Scholar] · doi:10.1177/0962280214537047
[17] Yousef WA, Kundu S, Wagner RF. Nonparametric estimation of the threshold at an operating point on the ROC curve. Comput Stat Data Anal. 2009;33(12):4370-4383. doi: 10.1016/j.csda.2009.06.006[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1453.62259 · doi:10.1016/j.csda.2009.06.006
[18] Martínez-Camblor P. Nonparametric cut-off point estimation for diagnostic decisions with weighted errors. Rev Colombiana Estadística. 2011;34(1):133-146. [Google Scholar] · Zbl 07578252
[19] Blanche P, Dartigues JF, Jacqmin-Gaddal H. Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring. Biom J. 2013;5:687-704. doi: 10.1002/bimj.201200045[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1400.62250
[20] Heagerty PJ, Lumley T, Pepe MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics. 2000;56:337-344. doi: 10.1111/j.0006-341X.2000.00337.x[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1060.62622
[21] Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Ann Stat. 1994;22(3):1299-1327. doi: 10.1214/aos/1176325630[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0819.62028
[22] Uno H, Cai T, Tian L, Wei LJ. Evaluating prediction rules for t-Year survivors with censored regression models. J Am Stat Assoc. 2007;102(478):527-537. doi: 10.1198/016214507000000149[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1172.62327
[23] Hung H, Chiang CT. Estimation methods for time-dependent AUC models with survival data. Can J Stat. 2010;38(1):8-26. [Web of Science ®], [Google Scholar] · Zbl 1190.62084
[24] Cai T, Pepe MS, Zheng Y, Lumley T, Jenny NS. The sensitivity and specificity of markers for event times. Biostatistics. 2006;7(2):182-197. doi: 10.1093/biostatistics/kxi047[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1169.62367
[25] Etzioni R, Pepe MS, Longton G, Hu C, Goodman G. Incorporating the time dimension in receiver operating characteristic curves: a case study of prostate cancer. Med Decis Mak. 1999;19:242-251. doi: 10.1177/0272989X9901900303[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[26] Marin JM, Alfageme I, Almagro P, et al. Multicomponent indices to predict mortality in COPD: the COCOMICS study. Eur Respiratory J. 2013;42:323-332. doi: 10.1183/09031936.00121012[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[27] Klein JP, Moeschberger ML. Survival analysis: techniques for censored and truncated data. New York: Springer; 2003. [Google Scholar] · Zbl 1011.62106
[28] Soriano J, Alfageme I, Almagro P, Casanova C, et al. Distribution and prognostic validity of the new global initiative for chronic obstructive lung disease grading classification. Chest. 2013;143(3):694-702. doi: 10.1378/chest.12-1053[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[29] Martínez-Camblor P, Corral N, Rey C, Pascual J, Cernuda-Morollón E. ROC curve generalization for non-monotone relationships. Stat Methods Med Res. 2014, doi:10.1177/0962280214541095. [Google Scholar] · doi:10.1177/0962280214541095
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