Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks
The area under the time‐dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with sub...
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| Published in | Statistics in medicine Vol. 32; no. 30; pp. 5381 - 5397 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
30.12.2013
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.5958 |
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| Abstract | The area under the time‐dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The ‘timeROC’ R package is provided to make the methodology easily usable. Copyright © 2013 John Wiley & Sons, Ltd. |
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| AbstractList | The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The "timeROC" R package is provided to make the methodology easily usable. [PUBLICATION ABSTRACT] The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The "timeROC" R package is provided to make the methodology easily usable. The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable.The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable. The area under the time‐dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The ‘timeROC’ R package is provided to make the methodology easily usable. Copyright © 2013 John Wiley & Sons, Ltd. |
| Author | Dartigues, Jean-François Jacqmin-Gadda, Hélène Blanche, Paul |
| Author_xml | – sequence: 1 givenname: Paul surname: Blanche fullname: Blanche, Paul email: Correspondence to: Paul Blanche, INSERM U897 - Equipe de biostatistique, ISPED, Université Bordeaux Segalen, 146 rue Leo Saignat, 33076 Bordeaux cedex, France., Paul.Blanche@isped.u-bordeaux2.fr organization: University Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique, F-33000 Bordeaux, France – sequence: 2 givenname: Jean-François surname: Dartigues fullname: Dartigues, Jean-François organization: University Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique, F-33000 Bordeaux, France – sequence: 3 givenname: Hélène surname: Jacqmin-Gadda fullname: Jacqmin-Gadda, Hélène organization: University Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique, F-33000 Bordeaux, France |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/24027076$$D View this record in MEDLINE/PubMed |
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| ContentType | Journal Article |
| Copyright | Copyright © 2013 John Wiley & Sons, Ltd. Copyright Wiley Subscription Services, Inc. Dec 30, 2013 |
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| DOI | 10.1002/sim.5958 |
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| Keywords | competing risks discrimination survival analysis prognosis inverse probability of censoring weighting AUC |
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| References | Zheng Y, Cai T, Jin Y, Feng Z. Evaluating prognostic accuracy of biomarkers under competing risk. Biometrics 2012; 68(2):388-396. DOI: 10.1111/j.1541-0420.2011.01671.x. Cai T, Pepe MS. Semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease. Journal of the American Statistical Association 2002; 97(460):1099-1107. DOI: 10.1198/016214502388618915. DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves : a nonparametric approach. Biometrics 1988; 44(3):837-845. Heagerty P, Lumley T, Pepe M. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 2000; 56(2):337-344. DOI: 10.1111/j.0006-341X.2000.00337.x. Bretz F, Hothorn T, Westfall P. Multiple Comparisons Using R. CRC press, Boca Raton, 2010. Martinussen T, Scheike TH. Dynamic Regression Models for Survival Data. Springer: New York, 2006. Wechsler D. Wechsler Adult Intelligence Scale (rev. ed.) Psychological Corporation: New York, 1981. Blanche P, Dartigues JF, Jacqmin-Gadda H. Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring. Biometrical Journal 2013. DOI: 10.1002/bimj.201200045. in press. Pepe M. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press: Oxford, 2003. Kerr KF, Pepe MS. Joint modeling, covariate adjustment, and interaction: contrasting notions in risk prediction models and risk prediction performance. Epidemiology 2011; 22(6):805-812. DOI: 10.1097/EDE.0b013e31823035fb. Van der Laan MJ, Robins JM. Unified Methods for Censored Longitudinal Data and Causality. Springer Verlag: New York, 2003. Tsiatis AA. Semiparametric Theory and Missing Data. Springer Verlag: New York, 2006. Folstein MF, Folstein SE, McHugh PR et al. "Mini-mental state". A practical method for grading the cognitive state of patients for the clinician. Journal of Psychiatric Research 1975; 12(3):189-198. Aalen O, Borgan Ø, Gjessing HK, Gjessing S. Survival and Event History Analysis: A Process Point of View. Springer, 2008. Amieva H, Jacqmin-Gadda H, Orgogozo J, Le Carret N, Helmer C, Letenneur L, Barberger-Gateau P, Fabrigoule C, Dartigues J. The 9-year cognitive decline before dementia of the Alzheimer type: a prospective population-based study. Brain 2005; 128(5):1093. DOI: 10.1093/brain/awh451. Hung H, Chiang CT. Estimation methods for time-dependent AUC models with survival data. Canadian Journal of Statistics 2010; 38(1):8-26. DOI: 10.1002/cjs.10046. Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Annals of Statistics 1994; 22: 1299-1327. Robins JM, Ritov Y. Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statistics in Medicine 1997; 16: 285-319. Dartigues JF, Gagnon M, Barberger-Gateau P, Letenneur L, Commenges D, Sauvel C, Michel P, Salamon R. The PAQUID epidemiological program on brain ageing. Neuroepidemiology 1992; 11(1):14-18. Saha P, Heagerty P. Time-dependent predictive accuracy in the presence of competing risks. Biometrics 2010; 66(4):999-1011. DOI: 10.1111/j.1541-0420.2009.01375.x. Foucher Y, Giral M, Soulillou JP, Daures JP. Time-dependent ROC analysis for a three-class prognostic with application to kidney transplantation. Statistics in Medicine 2010; 29(30):3079-3087. DOI: 10.1002/sim.4052. Chiang C, Hung H. Non-parametric estimation for time-dependent AUC. Journal of Statistical Planning and Inference 2010; 140(5):1162-1174. DOI: 10.1016/j.jspi.2009.10.012. 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. Steyerberg EW. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating. Springer: New York, 2009. Satten GA, Datta S. The Kaplan-Meier estimator as an inverse-probability-of-censoring weighted average. The American Statistician 2001; 55(3):207-210. DOI: 10.1198/000313001317098185. Jewell NP, Lei X, Ghani AC, Donnelly CA, Leung GM, Ho LM, Cowling BJ, Hedley AJ. Non-parametric estimation of the case fatality ratio with competing risks data: an application to severe acute respiratory syndrome (SARS). Statistics in Medicine 2007; 26(9):1982-1998. DOI: 10.1002/sim.2691. Scheike T, Zhang M, Gerds T. Predicting cumulative incidence probability by direct binomial regression. Biometrika 2008; 95: 205-220. DOI: 10.1093/biomet/asm096. Aisen P, Andrieu S, Sampaio C, Carrillo M, Khachaturian Z, Dubois B, Feldman H, Petersen R, Siemers E, Doody R, et al. Report of the task force on designing clinical trials in early (predementia) AD. Neurology 2011; 76(3):280-286. DOI: 10.1212/WNL.0b013e318207b1b9. Uno H, Cai T, Tian L, Wei LJ. Evaluating prediction rules for t-year survivors with censored regression models. Journal of the American Statistical Association 2007; 102(478):527-537. DOI: 10.1198/016214507000000149. Lin DY, Fleming TR, Wei LJ. Confidence bands for survival curves under the proportional hazards model. Biometrika 1994; 81(1):73-81. Joly P, Commenges D, Helmer C, Letenneur L. A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics 2002; 3(3):433. DOI: 10.1093/biostatistics/3.3.433. Beyersmann J, Latouche A, Buchholz A, Schumacher M. Simulating competing risks data in survival analysis. Statistics in Medicine 2009; 28(6):956-971. DOI: 10.1002/sim.3516. 2007; 102 2010; 38 2002; 97 2010 2009 1994; 22 1975; 12 2008 2002; 3 2011; 76 2006 2010; 140 2003 2005; 61 1994; 81 2008; 95 1992; 11 2009; 28 2010; 66 2000; 56 2010; 29 2005; 128 1988; 44 2011; 22 1997; 16 1981 2013 2001; 55 2012; 68 2007; 26 e_1_2_10_23_1 e_1_2_10_24_1 e_1_2_10_21_1 e_1_2_10_20_1 Wechsler D (e_1_2_10_28_1) 1981 Pepe M (e_1_2_10_8_1) 2003 e_1_2_10_2_1 e_1_2_10_4_1 e_1_2_10_18_1 e_1_2_10_3_1 e_1_2_10_19_1 e_1_2_10_6_1 Martinussen T (e_1_2_10_22_1) 2006 e_1_2_10_5_1 e_1_2_10_17_1 e_1_2_10_14_1 e_1_2_10_7_1 e_1_2_10_15_1 e_1_2_10_36_1 e_1_2_10_12_1 e_1_2_10_35_1 e_1_2_10_9_1 e_1_2_10_13_1 Tsiatis AA (e_1_2_10_16_1) 2006 e_1_2_10_34_1 e_1_2_10_10_1 e_1_2_10_33_1 e_1_2_10_11_1 e_1_2_10_32_1 e_1_2_10_31_1 e_1_2_10_30_1 e_1_2_10_29_1 e_1_2_10_27_1 e_1_2_10_25_1 e_1_2_10_26_1 |
| References_xml | – reference: DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves : a nonparametric approach. Biometrics 1988; 44(3):837-845. – reference: Heagerty P, Lumley T, Pepe M. Time-dependent ROC curves for censored survival data and a diagnostic marker. Biometrics 2000; 56(2):337-344. DOI: 10.1111/j.0006-341X.2000.00337.x. – reference: 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. – reference: Amieva H, Jacqmin-Gadda H, Orgogozo J, Le Carret N, Helmer C, Letenneur L, Barberger-Gateau P, Fabrigoule C, Dartigues J. The 9-year cognitive decline before dementia of the Alzheimer type: a prospective population-based study. Brain 2005; 128(5):1093. DOI: 10.1093/brain/awh451. – reference: Beyersmann J, Latouche A, Buchholz A, Schumacher M. Simulating competing risks data in survival analysis. Statistics in Medicine 2009; 28(6):956-971. DOI: 10.1002/sim.3516. – reference: Dartigues JF, Gagnon M, Barberger-Gateau P, Letenneur L, Commenges D, Sauvel C, Michel P, Salamon R. The PAQUID epidemiological program on brain ageing. Neuroepidemiology 1992; 11(1):14-18. – reference: Zheng Y, Cai T, Jin Y, Feng Z. Evaluating prognostic accuracy of biomarkers under competing risk. Biometrics 2012; 68(2):388-396. DOI: 10.1111/j.1541-0420.2011.01671.x. – reference: Kerr KF, Pepe MS. Joint modeling, covariate adjustment, and interaction: contrasting notions in risk prediction models and risk prediction performance. Epidemiology 2011; 22(6):805-812. DOI: 10.1097/EDE.0b013e31823035fb. – reference: Uno H, Cai T, Tian L, Wei LJ. Evaluating prediction rules for t-year survivors with censored regression models. Journal of the American Statistical Association 2007; 102(478):527-537. DOI: 10.1198/016214507000000149. – reference: Robins JM, Ritov Y. Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statistics in Medicine 1997; 16: 285-319. – reference: Scheike T, Zhang M, Gerds T. Predicting cumulative incidence probability by direct binomial regression. Biometrika 2008; 95: 205-220. DOI: 10.1093/biomet/asm096. – reference: Satten GA, Datta S. The Kaplan-Meier estimator as an inverse-probability-of-censoring weighted average. The American Statistician 2001; 55(3):207-210. DOI: 10.1198/000313001317098185. – reference: Van der Laan MJ, Robins JM. Unified Methods for Censored Longitudinal Data and Causality. Springer Verlag: New York, 2003. – reference: Aalen O, Borgan Ø, Gjessing HK, Gjessing S. Survival and Event History Analysis: A Process Point of View. Springer, 2008. – reference: Hung H, Chiang CT. Estimation methods for time-dependent AUC models with survival data. Canadian Journal of Statistics 2010; 38(1):8-26. DOI: 10.1002/cjs.10046. – reference: Joly P, Commenges D, Helmer C, Letenneur L. A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics 2002; 3(3):433. DOI: 10.1093/biostatistics/3.3.433. – reference: Bretz F, Hothorn T, Westfall P. Multiple Comparisons Using R. CRC press, Boca Raton, 2010. – reference: Saha P, Heagerty P. Time-dependent predictive accuracy in the presence of competing risks. Biometrics 2010; 66(4):999-1011. DOI: 10.1111/j.1541-0420.2009.01375.x. – reference: Blanche P, Dartigues JF, Jacqmin-Gadda H. Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring. Biometrical Journal 2013. DOI: 10.1002/bimj.201200045. in press. – reference: Jewell NP, Lei X, Ghani AC, Donnelly CA, Leung GM, Ho LM, Cowling BJ, Hedley AJ. Non-parametric estimation of the case fatality ratio with competing risks data: an application to severe acute respiratory syndrome (SARS). Statistics in Medicine 2007; 26(9):1982-1998. DOI: 10.1002/sim.2691. – reference: Steyerberg EW. Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating. Springer: New York, 2009. – reference: Pepe M. The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press: Oxford, 2003. – reference: Martinussen T, Scheike TH. Dynamic Regression Models for Survival Data. Springer: New York, 2006. – reference: Aisen P, Andrieu S, Sampaio C, Carrillo M, Khachaturian Z, Dubois B, Feldman H, Petersen R, Siemers E, Doody R, et al. Report of the task force on designing clinical trials in early (predementia) AD. Neurology 2011; 76(3):280-286. DOI: 10.1212/WNL.0b013e318207b1b9. – reference: Foucher Y, Giral M, Soulillou JP, Daures JP. Time-dependent ROC analysis for a three-class prognostic with application to kidney transplantation. Statistics in Medicine 2010; 29(30):3079-3087. DOI: 10.1002/sim.4052. – reference: Chiang C, Hung H. Non-parametric estimation for time-dependent AUC. Journal of Statistical Planning and Inference 2010; 140(5):1162-1174. DOI: 10.1016/j.jspi.2009.10.012. – reference: Lin DY, Fleming TR, Wei LJ. Confidence bands for survival curves under the proportional hazards model. Biometrika 1994; 81(1):73-81. – reference: Akritas MG. Nearest neighbor estimation of a bivariate distribution under random censoring. Annals of Statistics 1994; 22: 1299-1327. – reference: Wechsler D. Wechsler Adult Intelligence Scale (rev. ed.) Psychological Corporation: New York, 1981. – reference: Tsiatis AA. Semiparametric Theory and Missing Data. Springer Verlag: New York, 2006. – reference: Cai T, Pepe MS. Semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease. Journal of the American Statistical Association 2002; 97(460):1099-1107. DOI: 10.1198/016214502388618915. – reference: Folstein MF, Folstein SE, McHugh PR et al. "Mini-mental state". A practical method for grading the cognitive state of patients for the clinician. Journal of Psychiatric Research 1975; 12(3):189-198. – year: 2009 – volume: 102 start-page: 527 issue: 478 year: 2007 end-page: 537 article-title: Evaluating prediction rules for t‐year survivors with censored regression models publication-title: Journal of the American Statistical Association – year: 1981 – volume: 12 start-page: 189 issue: 3 year: 1975 end-page: 198 article-title: “Mini‐mental state”. A practical method for grading the cognitive state of patients for the clinician publication-title: Journal of Psychiatric Research – volume: 128 start-page: 1093 issue: 5 year: 2005 article-title: The 9‐year cognitive decline before dementia of the Alzheimer type: a prospective population‐based study publication-title: Brain – volume: 29 start-page: 3079 issue: 30 year: 2010 end-page: 3087 article-title: Time‐dependent ROC analysis for a three‐class prognostic with application to kidney transplantation publication-title: Statistics in Medicine – year: 2003 – volume: 56 start-page: 337 issue: 2 year: 2000 end-page: 344 article-title: Time‐dependent ROC curves for censored survival data and a diagnostic marker publication-title: Biometrics – volume: 38 start-page: 8 issue: 1 year: 2010 end-page: 26 article-title: Estimation methods for time‐dependent AUC models with survival data publication-title: Canadian Journal of Statistics – volume: 26 start-page: 1982 issue: 9 year: 2007 end-page: 1998 article-title: Non‐parametric estimation of the case fatality ratio with competing risks data: an application to severe acute respiratory syndrome (SARS) publication-title: Statistics in Medicine – year: 2010 – volume: 76 start-page: 280 issue: 3 year: 2011 end-page: 286 article-title: Report of the task force on designing clinical trials in early (predementia) AD publication-title: Neurology – volume: 95 start-page: 205 year: 2008 end-page: 220 article-title: Predicting cumulative incidence probability by direct binomial regression publication-title: Biometrika – volume: 68 start-page: 388 issue: 2 year: 2012 end-page: 396 article-title: Evaluating prognostic accuracy of biomarkers under competing risk publication-title: Biometrics – volume: 22 start-page: 1299 year: 1994 end-page: 1327 article-title: Nearest neighbor estimation of a bivariate distribution under random censoring publication-title: Annals of Statistics – volume: 3 start-page: 433 issue: 3 year: 2002 article-title: A penalized likelihood approach for an illness–death model with interval‐censored data: application to age‐specific incidence of dementia publication-title: Biostatistics – volume: 44 start-page: 837 issue: 3 year: 1988 end-page: 845 article-title: Comparing the areas under two or more correlated receiver operating characteristic curves : a nonparametric approach publication-title: Biometrics – year: 2008 – year: 2006 – year: 2013 article-title: Review and comparison of ROC curve estimators for a time‐dependent outcome with marker‐dependent censoring publication-title: Biometrical Journal – volume: 81 start-page: 73 issue: 1 year: 1994 end-page: 81 article-title: Confidence bands for survival curves under the proportional hazards model publication-title: Biometrika – volume: 97 start-page: 1099 issue: 460 year: 2002 end-page: 1107 article-title: Semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease publication-title: Journal of the American Statistical Association – volume: 22 start-page: 805 issue: 6 year: 2011 end-page: 812 article-title: Joint modeling, covariate adjustment, and interaction: contrasting notions in risk prediction models and risk prediction performance publication-title: Epidemiology – volume: 140 start-page: 1162 issue: 5 year: 2010 end-page: 1174 article-title: Non‐parametric estimation for time‐dependent AUC publication-title: Journal of Statistical Planning and Inference – volume: 16 start-page: 285 year: 1997 end-page: 319 article-title: Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi‐parametric models publication-title: Statistics in Medicine – volume: 61 start-page: 92 issue: 1 year: 2005 end-page: 105 article-title: Survival model predictive accuracy and ROC curves publication-title: Biometrics – volume: 66 start-page: 999 issue: 4 year: 2010 end-page: 1011 article-title: Time‐dependent predictive accuracy in the presence of competing risks publication-title: Biometrics – volume: 28 start-page: 956 issue: 6 year: 2009 end-page: 971 article-title: Simulating competing risks data in survival analysis publication-title: Statistics in Medicine – volume: 55 start-page: 207 issue: 3 year: 2001 end-page: 210 article-title: The Kaplan‐Meier estimator as an inverse‐probability‐of‐censoring weighted average publication-title: The American Statistician – volume: 11 start-page: 14 issue: 1 year: 1992 end-page: 18 article-title: The PAQUID epidemiological program on brain ageing publication-title: Neuroepidemiology – year: 2013 – ident: e_1_2_10_9_1 doi: 10.2307/2531595 – ident: e_1_2_10_17_1 doi: 10.1002/sim.2691 – ident: e_1_2_10_23_1 doi: 10.1201/9781420010909 – ident: e_1_2_10_31_1 doi: 10.1007/978-0-387-77244-8 – ident: e_1_2_10_10_1 doi: 10.1198/016214507000000149 – ident: e_1_2_10_11_1 doi: 10.1002/cjs.10046 – volume-title: The Statistical Evaluation of Medical Tests for Classification and Prediction year: 2003 ident: 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| Snippet | The area under the time‐dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For... The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For... |
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| Title | Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks |
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