Skip to main content
Top
Published in: BMC Medical Research Methodology 1/2017

Open Access 01-12-2017 | Research article

Time-dependent ROC curve analysis in medical research: current methods and applications

Authors: Adina Najwa Kamarudin, Trevor Cox, Ruwanthi Kolamunnage-Dona

Published in: BMC Medical Research Methodology | Issue 1/2017

Login to get access

Abstract

Background

ROC (receiver operating characteristic) curve analysis is well established for assessing how well a marker is capable of discriminating between individuals who experience disease onset and individuals who do not. The classical (standard) approach of ROC curve analysis considers event (disease) status and marker value for an individual as fixed over time, however in practice, both the disease status and marker value change over time. Individuals who are disease-free earlier may develop the disease later due to longer study follow-up, and also their marker value may change from baseline during follow-up. Thus, an ROC curve as a function of time is more appropriate. However, many researchers still use the standard ROC curve approach to determine the marker capability ignoring the time dependency of the disease status or the marker.

Methods

We comprehensively review currently proposed methodologies of time-dependent ROC curves which use single or longitudinal marker measurements, aiming to provide clarity in each methodology, identify software tools to carry out such analysis in practice and illustrate several applications of the methodology. We have also extended some methods to incorporate a longitudinal marker and illustrated the methodologies using a sequential dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver.

Results

From our methodological review, we have identified 18 estimation methods of time-dependent ROC curve analyses for censored event times and three other methods can only deal with non-censored event times. Despite the considerable numbers of estimation methods, applications of the methodology in clinical studies are still lacking.

Conclusions

The value of time-dependent ROC curve methods has been re-established. We have illustrated the methods in practice using currently available software and made some recommendations for future research.
Appendix
Available only for authorised users
Literature
1.
go back to reference Heagerty PJ, Lumley T, Pepe MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics. 2000;56(2):337–44.CrossRefPubMed Heagerty PJ, Lumley T, Pepe MS. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics. 2000;56(2):337–44.CrossRefPubMed
2.
go back to reference Hung H, Chiang CT. Estimation methods for time-dependent AUC models with survival data. Can J Stat Revue Can Stat. 2010;38(1):8–26. Hung H, Chiang CT. Estimation methods for time-dependent AUC models with survival data. Can J Stat Revue Can Stat. 2010;38(1):8–26.
3.
4.
go back to reference Chambless LE, Diao G. Estimation of time-dependent area under the ROC curve for long-term risk prediction. Stat Med. 2006;25(20):3474–86.CrossRefPubMed Chambless LE, Diao G. Estimation of time-dependent area under the ROC curve for long-term risk prediction. Stat Med. 2006;25(20):3474–86.CrossRefPubMed
5.
go back to reference Lambert J, Chevret S. Summary measure of discrimination in survival models based on cumulative/dynamic time-dependent ROC curves. Stat Methods In Med Res. 2014;25(5):2088–102. Lambert J, Chevret S. Summary measure of discrimination in survival models based on cumulative/dynamic time-dependent ROC curves. Stat Methods In Med Res. 2014;25(5):2088–102.
6.
go back to reference Cai T, Pepe MS, Lumley T, Zheng Y, Jenny NJ. The sensitivity and specificity of markers for event times. Biostatistics. 2006;7(2):182–97.CrossRefPubMed Cai T, Pepe MS, Lumley T, Zheng Y, Jenny NJ. The sensitivity and specificity of markers for event times. Biostatistics. 2006;7(2):182–97.CrossRefPubMed
8.
go back to reference Pepe MS. The statistical evaluation of medical tests for classification and prediction. USA: Oxford University Press; 2003. Pepe MS. The statistical evaluation of medical tests for classification and prediction. USA: Oxford University Press; 2003.
9.
go back to reference Zheng Y, Heagerty PJ. Semiparametric estimation of time-dependent ROC curves for longitudinal marker data. Biostatistics. 2004;5(4):615–32.CrossRefPubMed Zheng Y, Heagerty PJ. Semiparametric estimation of time-dependent ROC curves for longitudinal marker data. Biostatistics. 2004;5(4):615–32.CrossRefPubMed
10.
go back to reference Bamber D. The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. J Math Psychol. 1975;12(4):387–415.CrossRef Bamber D. The area above the ordinal dominance graph and the area below the receiver operating characteristic graph. J Math Psychol. 1975;12(4):387–415.CrossRef
11.
go back to reference Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology. 1982;143(1):29–36.CrossRefPubMed Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology. 1982;143(1):29–36.CrossRefPubMed
12.
go back to reference Heagerty PJ, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics. 2005;61(1):92–105.CrossRefPubMed Heagerty PJ, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics. 2005;61(1):92–105.CrossRefPubMed
13.
go back to reference 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. 2013;55(5):687–704.CrossRefPubMed 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. 2013;55(5):687–704.CrossRefPubMed
14.
go back to reference Zheng Y, Heagerty PJ. Prospective accuracy for longitudinal markers. Biometrics. 2007;63(2):332–41.CrossRefPubMed Zheng Y, Heagerty PJ. Prospective accuracy for longitudinal markers. Biometrics. 2007;63(2):332–41.CrossRefPubMed
15.
go back to reference Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53(282):457–81.CrossRef Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53(282):457–81.CrossRef
16.
go back to reference Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Ann Stat. 1994;1299–1327. Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Ann Stat. 1994;1299–1327.
17.
go back to reference Cai T, Gerds TA, Zheng Y, Chen J. Robust Prediction of t‐Year Survival with Data from Multiple Studies. Biometrics. 2011;67(2):436–44.CrossRefPubMed Cai T, Gerds TA, Zheng Y, Chen J. Robust Prediction of t‐Year Survival with Data from Multiple Studies. Biometrics. 2011;67(2):436–44.CrossRefPubMed
18.
go back to reference Hung H, Chiang CT. Optimal Composite Markers for Time-Dependent Receiver Operating Characteristic Curves with Censored Survival Data. Scand J Stat. 2010;37(4):664–79.CrossRef Hung H, Chiang CT. Optimal Composite Markers for Time-Dependent Receiver Operating Characteristic Curves with Censored Survival Data. Scand J Stat. 2010;37(4):664–79.CrossRef
19.
go back to reference Song X, Zhou XH. A semiparametric approach for the covariate specific ROC curve with survival outcome. Statistica Sinica. 2008;18(3):947-65. Song X, Zhou XH. A semiparametric approach for the covariate specific ROC curve with survival outcome. Statistica Sinica. 2008;18(3):947-65.
20.
go back to reference Viallon V, Latouche A. Discrimination measures for survival outcomes: connection between the AUC and the predictiveness curve. Biom J. 2011;53(2):217–36.CrossRefPubMed Viallon V, Latouche A. Discrimination measures for survival outcomes: connection between the AUC and the predictiveness curve. Biom J. 2011;53(2):217–36.CrossRefPubMed
21.
go back to reference Uno H, Cai TX, Tian L, Wei LJ. Evaluating prediction rules for t-year survivors with censored regression models. J Am Stat Assoc. 2007;102(478):527–37. Uno H, Cai TX, Tian L, Wei LJ. Evaluating prediction rules for t-year survivors with censored regression models. J Am Stat Assoc. 2007;102(478):527–37.
22.
go back to reference Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med. 2011;30(19):2409–21.CrossRefPubMed Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med. 2011;30(19):2409–21.CrossRefPubMed
23.
go back to reference Cox DR. lRegression Models and Life Tables. mJ R Stat Soc Ser B. 1972;34(2):187–220. Cox DR. lRegression Models and Life Tables. mJ R Stat Soc Ser B. 1972;34(2):187–220.
24.
25.
go back to reference Cai Z, Sun Y. Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models. Scand J Stat. 2003;30(1):93–111.CrossRef Cai Z, Sun Y. Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models. Scand J Stat. 2003;30(1):93–111.CrossRef
26.
go back to reference Grambsch PM, Therneau TM. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika. 1994;81(3):515–26.CrossRef Grambsch PM, Therneau TM. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika. 1994;81(3):515–26.CrossRef
27.
go back to reference Xu R, O'Quigley J. Proportional hazards estimate of the conditional survival function. J R Stat Soc Ser B (Stat Methodol). 2000;62(4):667–80.CrossRef Xu R, O'Quigley J. Proportional hazards estimate of the conditional survival function. J R Stat Soc Ser B (Stat Methodol). 2000;62(4):667–80.CrossRef
28.
go back to reference Saha-Chaudhuri P, Heagerty PJ. Non-parametric estimation of a time-dependent predictive accuracy curve. Biostatistics. 2013;14(1):42–59.CrossRefPubMed Saha-Chaudhuri P, Heagerty PJ. Non-parametric estimation of a time-dependent predictive accuracy curve. Biostatistics. 2013;14(1):42–59.CrossRefPubMed
29.
30.
go back to reference Royston P, Altman DG. Regression Using Fractional Polynomials of Continuous Covariates - Parsimonious Parametric Modeling. Appl Stat-J Roy St C. 1994;43(3):429-67. Royston P, Altman DG. Regression Using Fractional Polynomials of Continuous Covariates - Parsimonious Parametric Modeling. Appl Stat-J Roy St C. 1994;43(3):429-67.
31.
go back to reference Leisenring W, Pepe MS, Longton G. A marginal regression modelling framework for evaluating medical diagnostic tests. Stat Med. 1997;16(11):1263–81.CrossRefPubMed Leisenring W, Pepe MS, Longton G. A marginal regression modelling framework for evaluating medical diagnostic tests. Stat Med. 1997;16(11):1263–81.CrossRefPubMed
32.
go back to reference Etzioni R, Pepe M, 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(3):242–51.CrossRef Etzioni R, Pepe M, 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(3):242–51.CrossRef
33.
go back to reference Tosteson ANA, Begg CB. A general regression methodology for ROC curve estimation. Med Decis Mak. 1988;8(3):204–15.CrossRef Tosteson ANA, Begg CB. A general regression methodology for ROC curve estimation. Med Decis Mak. 1988;8(3):204–15.CrossRef
34.
go back to reference Pepe MS. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics. 1998; 54(1):124-35. Pepe MS. Three approaches to regression analysis of receiver operating characteristic curves for continuous test results. Biometrics. 1998; 54(1):124-35.
35.
go back to reference Heagerty PJ, Pepe MS. Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children. J R Stat Soc: Ser C: Appl Stat. 1999;48(4):533–51.CrossRef Heagerty PJ, Pepe MS. Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children. J R Stat Soc: Ser C: Appl Stat. 1999;48(4):533–51.CrossRef
36.
go back to reference Yang S-S. Linear combination of concomitants of order statistics with application to testing and estimation. Ann Inst Stat Math. 1981;33(1):463–70.CrossRef Yang S-S. Linear combination of concomitants of order statistics with application to testing and estimation. Ann Inst Stat Math. 1981;33(1):463–70.CrossRef
37.
go back to reference Zheng Y, Heagerty PJ. Partly conditional survival models for longitudinal data. Biometrics. 2005;61(2):379–91.CrossRefPubMed Zheng Y, Heagerty PJ. Partly conditional survival models for longitudinal data. Biometrics. 2005;61(2):379–91.CrossRefPubMed
38.
go back to reference Heagerty PJ, Saha-Chaudhuri P, Saha-Chaudhuri MP. Package ‘survivalROC’. 2013. Heagerty PJ, Saha-Chaudhuri P, Saha-Chaudhuri MP. Package ‘survivalROC’. 2013.
39.
go back to reference Potapov S, Adler W, Schmid M: survAUC: Estimators of Prediction Accuracy for Time-to-Event Data. R package version 1.0-5. In.; 2012. Potapov S, Adler W, Schmid M: survAUC: Estimators of Prediction Accuracy for Time-to-Event Data. R package version 1.0-5. In.; 2012.
41.
go back to reference Therneau TM, Lumley T. Package ‘survival’. In.: Verze; 2015 Therneau TM, Lumley T. Package ‘survival’. In.: Verze; 2015
42.
go back to reference Scheike T. Timereg Package. In.: R Package Version; 2009. Scheike T. Timereg Package. In.: R Package Version; 2009.
43.
go back to reference Gerds TA, Rcpp I, Rcpp L, Gerds MTA. Package ‘prodlim’. 2015. Gerds TA, Rcpp I, Rcpp L, Gerds MTA. Package ‘prodlim’. 2015.
44.
go back to reference Heagerty PJ, Saha-Chaudhuri P, Saha-Chaudhuri MP. Package ‘risksetROC’. 2012. Heagerty PJ, Saha-Chaudhuri P, Saha-Chaudhuri MP. Package ‘risksetROC’. 2012.
45.
go back to reference Lu Y, Wang L, Liu P, Yang P, You M. Gene-expression signature predicts postoperative recurrence in stage I non-small cell lung cancer patients. PLoS One. 2012;7(1):e30880.CrossRefPubMedPubMedCentral Lu Y, Wang L, Liu P, Yang P, You M. Gene-expression signature predicts postoperative recurrence in stage I non-small cell lung cancer patients. PLoS One. 2012;7(1):e30880.CrossRefPubMedPubMedCentral
46.
go back to reference Tse LA, Dai JC, Chen MH, Liu YW, Zhang H, Wong TW, Leung CC, Kromhout H, Meijer E, Liu S et al. Prediction models and risk assessment for silicosis using a retrospective cohort study among workers exposed to silica in China. Scientific Reports. 2015;5. Tse LA, Dai JC, Chen MH, Liu YW, Zhang H, Wong TW, Leung CC, Kromhout H, Meijer E, Liu S et al. Prediction models and risk assessment for silicosis using a retrospective cohort study among workers exposed to silica in China. Scientific Reports. 2015;5.
47.
go back to reference Yue Y, Cui X, Bose S, Audeh W, Zhang X, Fraass B. Stratifying triple-negative breast cancer prognosis using 18 F-FDG-PET/CT imaging. Breast Cancer Res Treat. 2015;153(3):607–16.CrossRefPubMedPubMedCentral Yue Y, Cui X, Bose S, Audeh W, Zhang X, Fraass B. Stratifying triple-negative breast cancer prognosis using 18 F-FDG-PET/CT imaging. Breast Cancer Res Treat. 2015;153(3):607–16.CrossRefPubMedPubMedCentral
48.
go back to reference Yue Y, Astvatsaturyan K, Cui X, Zhang X, Fraass B, Bose S. Stratification of Prognosis of Triple-Negative Breast Cancer Patients Using Combinatorial Biomarkers. PLoS One. 2016;11(3):e0149661.CrossRefPubMedPubMedCentral Yue Y, Astvatsaturyan K, Cui X, Zhang X, Fraass B, Bose S. Stratification of Prognosis of Triple-Negative Breast Cancer Patients Using Combinatorial Biomarkers. PLoS One. 2016;11(3):e0149661.CrossRefPubMedPubMedCentral
49.
go back to reference Desmedt C, Giobbie-Hurder A, Neven P, Paridaens R, Christiaens M-R, Smeets A, Lallemand F, Haibe-Kains B, Viale G, Gelber RD. The Gene expression Grade Index: a potential predictor of relapse for endocrine-treated breast cancer patients in the BIG 1–98 trial. BMC Med Genet. 2009;2(1):1. Desmedt C, Giobbie-Hurder A, Neven P, Paridaens R, Christiaens M-R, Smeets A, Lallemand F, Haibe-Kains B, Viale G, Gelber RD. The Gene expression Grade Index: a potential predictor of relapse for endocrine-treated breast cancer patients in the BIG 1–98 trial. BMC Med Genet. 2009;2(1):1.
Metadata
Title
Time-dependent ROC curve analysis in medical research: current methods and applications
Authors
Adina Najwa Kamarudin
Trevor Cox
Ruwanthi Kolamunnage-Dona
Publication date
01-12-2017
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2017
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/s12874-017-0332-6

Other articles of this Issue 1/2017

BMC Medical Research Methodology 1/2017 Go to the issue