Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker
ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a ti...
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| Published in: | Biometrics Vol. 56; no. 2; pp. 337 - 344 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford, UK
Blackwell Publishing Ltd
01.06.2000
International Biometric Society |
| Subjects: | |
| ISSN: | 0006-341X, 1541-0420 |
| Online Access: | Get full text |
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| Abstract | ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. |
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| AbstractList | ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials.ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. ROC curves are a popular method for displaying sensitivity and specificity of a continuous marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t, and ROC curves that vary as a function of time may be mire appropriate. A common examples of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t= 0), by calculating ROC Curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimated for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. ROC curves are a popular method for displaying sensitivity and specificity of a continuous diagnostic marker, X, for a binary disease variable, D. However, many disease outcomes are time dependent, D(t), and ROC curves that vary as a function of time may be more appropriate. A common example of a time-dependent variable is vital status, where D(t) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X, measured at baseline (t = 0), by calculating ROC curves for cumulative disease or death incidence by time t, which we denote as ROC(t). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan-Meier estimator for each possible subset X > c. However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X. An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of (X, T), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22, 1299-1327). We present an example where ROC(t) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC(t) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. ROC curves are a popular method for displaying sensitivity and specificity of a continuous marker, X , for a binary disease variable, D. However, many disease outcomes are time dependent, D ( t , and ROC curves that vary as a function of time may be mire appropriate. A common examples of a time‐dependent variable is vital status, where D ( t ) = 1 if a patient has died prior to time t and zero otherwise. We propose summarizing the discrimination potential of a marker X , measured at baseline ( t = 0), by calculating ROC Curves for cumulative disease or death incidence by time t , which we denote as ROC( t ). A typical complexity with survival data is that observations may be censored. Two ROC curve estimators are proposed that can accommodate censored data. A simple estimator is based on using the Kaplan‐Meier estimated for each possible subset X > c . However, this estimator does not guarantee the necessary condition that sensitivity and specificity are monotone in X . An alternative estimator that does guarantee monotonicity is based on a nearest neighbor estimator for the bivariate distribution function of ( X, T ), where T represents survival time (Akritas, M. J., 1994, Annals of Statistics 22 , 1299–1327). We present an example where ROC( t ) is used to compare a standard and a modified flow cytometry measurement for predicting survival after detection of breast cancer and an example where the ROC( t ) curve displays the impact of modifying eligibility criteria for sample size and power in HIV prevention trials. |
| Author | Heagerty, Patrick J. Pepe, Margaret S. Lumley, Thomas |
| Author_xml | – sequence: 1 givenname: Patrick J. surname: Heagerty fullname: Heagerty, Patrick J. – sequence: 2 givenname: Thomas surname: Lumley fullname: Lumley, Thomas – sequence: 3 givenname: Margaret S. surname: Pepe fullname: Pepe, Margaret S. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/10877287$$D View this record in MEDLINE/PubMed |
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| CODEN | BIOMA5 |
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| References_xml | – reference: Hanley, J. A. (1989). Receiver operating characteristic (ROC) methodology: The state of the art. Critical Reviews in Diagnostic Imaging 29, 307-335. – reference: Zweig, M. H. and Campbell, G. (1993). Receiver-operator characteristic plots: A fundamental evaluation tool in clinical medicine. Clinical Chemistry 39, 561-577. – reference: Zhou, K. H., Hall, W. J., and Shapiro, D. E. (1997). Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. Statistics in Medicine 16, 2143-2156. – reference: Metz, C. E., Herman, B. A., and Shen, J. (1998). Maximum likelihood estimation of receiver operating characteristic (ROC) curves from continuously distributed data. Statistics in Medicine 17, 1033-1053. – reference: Pepe, M. S. (1997). A regression modelling framework for ROC curves in medical diagnostic testing. Biometrika 84, 595-608. – reference: Begg, C. G. (1987). Biases in the assessment of diagnostic tests. Statistics in Medicine 6, 411-423. – reference: van der Vaart, A. W. and Wellner, J. A. (1996). Weak Convergence and Empirical Processes with Applications to Statistics. New York : Springer. – reference: Swets, J. A. and Pickett, R. M. (1982). Evaluation of Diagnostic Systems: Methods from Signal Detection Theory. New York : Academic Press. – reference: Begg, C. G. (1991). Advances in statistical methodology for diagnostic medicine in the 1980's. Statistics in Medicine 10, 1887-1895. – reference: Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457-481. – reference: Akritas, M. G. (1994). Nearest neighbor estimation of a bivariate distribution under random censoring. Annals of Statistics 22, 1299-1327. – reference: Hanley, J. A. and McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143, 29-36. – reference: DeLong, E. R., DeLong, D. M., and Clarke-Pearson, D. L. (1988). Comparing the areas under two or more receiver operating characteristic curves: A nonparametric approach. Biometrics 44, 837-845. – reference: Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis. New York : Wiley. – reference: Sigurdsson, H., Baldetorp, B., Borg, A., Dalberg, M., Fernö, M., Killander, D., and Olsson, H. (1990). Indicators of prognosis in node-negative breast cancer. New England Journal of Medicine 322, 1045-53. – reference: Koblin, B., Heagerty, P., Sheon, A., Metzger, D., Buchbinder, S., Celum, C., Critchlow, C., Douglas, J., Gross, M., Marmor, M., Mayer, K., and Seage, G. (1998). Readiness of high-risk populations in the HIV network for prevention trials to participate in HIV-1 vaccine efficacy trials in the United States. AIDS 42, 785-793. – volume: 44 start-page: 837 year: 1988 end-page: 845 article-title: Comparing the areas under two or more receiver operating characteristic curves: A nonparametric approach publication-title: Biometrics – volume: 17 start-page: 1033 year: 1998 end-page: 1053 article-title: Maximum likelihood estimation of receiver operating characteristic (ROC) curves from continuously distributed data publication-title: Statistics in Medicine – volume: 322 start-page: 1045 year: 1990 end-page: 53 article-title: Indicators of prognosis in node‐negative breast cancer publication-title: New England Journal of Medicine – year: 1982 – 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: 10 start-page: 1887 year: 1991 end-page: 1895 article-title: Advances in statistical methodology for diagnostic medicine in the 1980's publication-title: Statistics in Medicine – volume: 18 start-page: 397 year: 1999 end-page: 422 – volume: 6 start-page: 411 year: 1987 end-page: 423 article-title: Biases in the assessment of diagnostic tests publication-title: Statistics in Medicine – volume: 53 start-page: 457 year: 1958 end-page: 481 article-title: Nonparametric estimation from incomplete observations publication-title: Journal of the American Statistical Association – volume: 42 start-page: 785 year: 1998 end-page: 793 article-title: Readiness of high‐risk populations in the HIV network for prevention trials to participate in HIV‐1 vaccine efficacy trials in the United States publication-title: AIDS – volume: 84 start-page: 595 year: 1997 end-page: 608 article-title: A regression modelling framework for ROC curves in medical diagnostic testing publication-title: Biometrika – volume: 29 start-page: 307 year: 1989 end-page: 335 article-title: Receiver operating characteristic (ROC) methodology: The state of the art publication-title: Critical Reviews in Diagnostic Imaging – volume: 143 start-page: 29 year: 1982 end-page: 36 article-title: The meaning and use of the area under a receiver operating characteristic (ROC) curve publication-title: Radiology – year: 1996 – volume: 16 start-page: 2143 year: 1997 end-page: 2156 article-title: Smooth non‐parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests publication-title: Statistics in Medicine – year: 1991 – volume: 4 start-page: 831 year: 1967 end-page: 853 – volume: 39 start-page: 561 year: 1993 end-page: 577 article-title: Receiver‐operator characteristic plots: A fundamental evaluation tool in clinical medicine publication-title: Clinical Chemistry – ident: e_1_2_1_2_1 doi: 10.1214/aos/1176325630 – ident: e_1_2_1_18_1 doi: 10.1002/(SICI)1097-0258(19971015)16:19<2143::AID-SIM655>3.0.CO;2-3 – ident: e_1_2_1_4_1 doi: 10.1002/sim.4780101205 – start-page: 397 volume-title: Handbook of Biostatistics year: 1999 ident: e_1_2_1_14_1 – ident: e_1_2_1_11_1 doi: 10.1097/00002030-199807000-00015 – ident: e_1_2_1_13_1 doi: 10.1093/biomet/84.3.595 – ident: e_1_2_1_12_1 doi: 10.1002/(SICI)1097-0258(19980515)17:9<1033::AID-SIM784>3.0.CO;2-Z – ident: e_1_2_1_17_1 doi: 10.1007/978-1-4757-2545-2 – volume: 39 start-page: 561 year: 1993 ident: e_1_2_1_19_1 article-title: Receiver‐operator characteristic plots: A fundamental evaluation tool in clinical medicine publication-title: Clinical Chemistry doi: 10.1093/clinchem/39.4.561 – ident: e_1_2_1_3_1 doi: 10.1002/sim.4780060402 – start-page: 831 volume-title: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability year: 1967 ident: e_1_2_1_6_1 – volume-title: Counting Processes and Survival Analysis year: 1991 ident: e_1_2_1_7_1 – ident: e_1_2_1_10_1 doi: 10.1080/01621459.1958.10501452 – volume: 29 start-page: 307 year: 1989 ident: e_1_2_1_8_1 article-title: Receiver operating characteristic (ROC) methodology: The state of the art publication-title: Critical Reviews in Diagnostic Imaging – ident: e_1_2_1_9_1 doi: 10.1148/radiology.143.1.7063747 – ident: e_1_2_1_15_1 doi: 10.1056/NEJM199004123221505 – ident: e_1_2_1_5_1 doi: 10.2307/2531595 – volume-title: Evaluation of Diagnostic Systems: Methods from Signal Detection Theory year: 1982 ident: e_1_2_1_16_1 |
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| SubjectTerms | Accuracy biometry Breast cancer breast neoplasms Breast Neoplasms - diagnosis Breast Neoplasms - mortality Censored data Censorship Cytometry death Discrimination Estimators Female flow cytometry Health outcomes Humans Infections Kaplan Meier estimator Kernel smoothing patients prediction Reliability functions ROC Curve Sample size Sensitivity Sensitivity and Specificity Specificity Survival Analysis Survival Rate Time Factors Treatment Outcome |
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| Title | Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker |
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