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SmoothROCtime: an $$\mathsf{R}$$ package for time-dependent ROC curve estimation. (English) Zbl 07255809
Summary: The receiver operating characteristic (ROC) curve has become one of the most used tools for analyzing the diagnostic capacity of continuous biomarkers. When the studied outcome is a time-dependent variable two main generalizations have been proposed, based on properly extensions of the sensitivity and the specificity. Different procedures have been suggested for their estimation mainly under the presence of right censorship. Most of them have been implemented, as well, in diverse types of software, including $$\mathsf{R}$$ packages. This work focuses on the $$\mathsf{R}$$ implementation for the smooth estimation of time-dependent ROC curves. The theoretical connection between them through the joint distribution function of the biomarker and time-to-event variables prompts an approximation method: considered estimators are based on the bivariate kernel density estimator for the joint density function of the bidimensional variable (Marker, Time-to-event). The use of the package is illustrated with two real-world examples.
##### MSC:
 65C60 Computational problems in statistics (MSC2010)
##### Software:
ks; nsROC; pROC; R; risksetROC; ROCR; SmoothROCtime; survAUC; survivalROC; tdROC
Full Text:
##### References:
 [1] Akritas, MG, Nearest neighbor estimation of a bivariate distribution under random censoring, Ann Stat, 22, 3, 1299-1327 (1994) · Zbl 0819.62028 [2] Blanche, P.; Dartigues, J-F; Jacqmin-Gadda, H., Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks, Stat Med, 32, 30, 5381-5397 (2013) [3] Blanche, P.; Dartigues, JF; Jacqmin-Gadda, H., Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring, Biom J, 55, 5, 687-704 (2013) · Zbl 1400.62250 [4] Cai, T.; Pepe, MS; Zheng, Y.; Lumley, T.; Jenny, NS, The sensitivity and specificity of markers for event times, Biostatistics, 7, 2, 182-197 (2006) · Zbl 1169.62367 [5] Chambless, LE; Diao, G., Estimation of time-dependent area under the ROC curve for long-term risk prediction, Stat Med, 25, 20, 3474-3486 (2006) [6] Díaz-Coto S (2018) smoothROCtime: smooth time-dependent ROC curve estimation. R package version 0.1.0 [7] Duong T (2004) Bandwidth matrices for multivariate kernel density estimation. PhD thesis, University of Western Australia [8] Duong T (2019) ks: kernel smoothing. R package version 1.11.5 [9] 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, 19, 3, 242-251 (1999) [10] Green, DM; Swets, JA, Signal detection theory and psychophysics (1966), New York: Wiley, New York [11] Hanley, JA; McNeil, BJ, The meaning and use of the area under a receiver operating characteristic (ROC) curve, Radiology, 143, 1, 29-36 (1982) [12] Heagerty PJ, Saha-Chaudhuri P (2012) risksetROC: riskset ROC curve estimation from censored survival data. R package version 1.0.4 [13] Heagerty PJ, Saha-Chaudhuri P (2013) survivalROC: time-dependent ROC curve estimation from censored survival data. R package version 1.0.3 [14] Heagerty, PJ; Zheng, Y., Survival model predictive accuracy and ROC curves, Biometrics, 61, 1, 92-105 (2005) · Zbl 1077.62077 [15] Heagerty, PJ; Lumley, T.; Pepe, MS, Time-dependent ROC curves for censored survival data and a diagnostic marker, Biometrics, 56, 2, 337-344 (2000) · Zbl 1060.62622 [16] Hung, H.; Chiang, C-T, Optimal composite markers for time-dependent receiver operating characteristic curves with censored survival data, Scand J Stat, 37, 4, 664-679 (2010) · Zbl 1349.62547 [17] Krzanowski, WJ; Hand, DJ, ROC curves for continuous data (2009), London: Chapman & Hall/CRC, London [18] Li L, Wu C (2016) tdROC: nonparametric estimation of time-dependent ROC curve from right censored survival data. R package version 1.0 [19] Li, L.; Greene, T.; Hu, B., A simple method to estimate the time-dependent receiver operating characteristic curve and the area under the curve with right censored data, Stat Methods Med Res, 27, 8, 2264-2278 (2018) [20] Martínez-Camblor, P.; Pardo-Fernández, JC, Smooth time-dependent receiver operating characteristic curve estimators, Stat Methods Med Res, 27, 3, 651-674 (2018) [21] Martínez-Camblor, P.; Bayón, GF; Pérez-Fernández, S., Cumulative/dynamic ROC curve estimation, J Stat Comput Simul, 86, 17, 3582-3594 (2016) · Zbl 07184816 [22] Pepe, MS, The statistical evaluation of medical tests for classification and prediction (2003), Oxford: Oxford University Press, Oxford · Zbl 1039.62105 [23] Pérez-Fernández S (2018) nsROC: non-standard ROC curve analysis. R package version 1.1 [24] Pérez-Fernández, S.; Martínez Camblor, P.; Filzmoser, P.; Corral, N., nsROC: an R package for non-standard ROC curve analysis, R J, 10, 2, 55-77 (2018) [25] Potapov S, Adler W, Schmid M (2012) survAUC: estimators of prediction accuracy for time-to-event data. R package version 1.0-5 [26] Robin, X.; Turck, N.; Hainard, A.; Tiberti, N.; Lisacek, F.; Sanchez, J-C; Müller, M., pROC: an open-source package for R and S+ to analyze and compare ROC curves, BMC Bioinform, 12, 77, 1-8 (2011) [27] Scott, DW, Multivariate density estimation: theory, practice, and visualization (1992), Hoboken: Wiley, Hoboken · Zbl 0850.62006 [28] Silverman, BW, Density estimation for statistics and data analysis (1986), London: Chapman and Hall, London [29] Sing, T.; Sander, O.; Beerenwinkel, N.; Lengauer, T., ROCR: visualizing classifier performance in R, Bioinformatics, 21, 20, 7881 (2005) [30] Uno, H.; Cai, T.; Tian, L.; Wei, LJ, Evaluating prediction rules for t-year survivors with censored regression models, J Am Stat Assoc, 102, 478, 527-537 (2007) · Zbl 1172.62327 [31] Zhou, XH; McClish, DK; Obuchowski, NA, Statistical methods in diagnostic medicine (2002), Hoboken: Wiley, Hoboken · Zbl 1007.62092
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