Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time‐to‐Event Data
In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling...
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| Published in | Biometrics Vol. 67; no. 3; pp. 819 - 829 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Malden, USA
Blackwell Publishing Inc
01.09.2011
Wiley-Blackwell Blackwell Publishing Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0006-341X 1541-0420 1541-0420 |
| DOI | 10.1111/j.1541-0420.2010.01546.x |
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| Abstract | In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time‐to‐event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time‐to‐event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time‐to‐death using their longitudinal CD4 cell count measurements. |
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| AbstractList | In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time‐to‐event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time‐to‐event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time‐to‐death using their longitudinal CD4 cell count measurements. In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time-to-event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time-to-event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time-to-death using their longitudinal CD4 cell count measurements.In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time-to-event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time-to-event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time-to-death using their longitudinal CD4 cell count measurements. Summary In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time‐to‐event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time‐to‐event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time‐to‐death using their longitudinal CD4 cell count measurements. |
| Author | Rizopoulos, Dimitris |
| Author_xml | – sequence: 1 givenname: Dimitris surname: Rizopoulos fullname: Rizopoulos, Dimitris |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/21306352$$D View this record in MEDLINE/PubMed |
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| CODEN | BIOMA5 |
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| References | Elashoff, R., Li, G., and Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics 64, 762-771. Henderson, R., Diggle, P., and Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics 1, 465-480. Brown, E., Ibrahim, J., and DeGruttola, V. (2005). A flexible B-spline model for multiple longitudinal biomarkers and survival. Biometrics 61, 64-73. Harrell, F., Callif, R., Pryor, D., Lee, K., and Rosati, R. (1982). Evaluating the yield of medical tests. Journal of the American Medical Association 247, 2543-2546. Tseng, Y.-K., Hsieh, F., and Wang, J.-L. (2005). Joint modelling of accelerated failure time and longitudinal data. Biometrika 92, 587-603. Abrams, D., Goldman, A., Launer, C., Korvick, A., Neaton, J., Crane, L., Grodesky, M., Wakefield, S., Muth, K., Kornegay, S., Cohn, D., Harris, A., Luskin-Hawk, R., Markowitz, N., Sampson, J., Thompson, M., Deyton, L. and the Terry Beirn Community Programs for Clinical Research on AIDS. (1994). Comparative trial of didanosine and zalcitabine in patients with human immunodeficiency virus infection who are intolerant of or have failed zidovudine therapy. New England Journal of Medicine 330, 657-662. Tsiatis, A. and Davidian, M. (2004). Joint modeling of longitudinal and time-to-event data: An overview. Statistica Sinica 14, 809-834. Antolini, L., Boracchi, P., and Biganzoli, E. (2005). A time-dependent discrimination index for survival data. Statistics in Medicine 24, 3927-3944. Kalbfleisch, J. and Prentice, R. (2002). The Statistical Analysis of Failure Time Data, 2nd edition. New York : Wiley. Rizopoulos, D., Verbeke, G., and Lesaffre, E. (2009). Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society, Series B 71, 637-654. Rizopoulos, D., Verbeke, G., and Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika 95, 63-74. Ding, J. and Wang, J.-L. (2008). Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics 64, 546-556. Heagerty, P. and Zheng, Y. (2005). Survival model predictive accuracy and ROC curves. Biometrics 61, 92-105. Taylor, J., Yu, M., and Sandler, H. (2005). Individualized predictions of disease progression following radiation therapy for prostate cancer. Journal of Clinical Oncology 23, 816-825. Zheng, Y. and Heagerty, P. (2007). Prospective accuracy for longitudinal markers. Biometrics 63, 332-341. Goldman, A., Carlin, B., Crane, L., Launer, C., Korvick, J., Deyton, L., and Abrams, D. (1996). Response of CD4+ and clinical consequences to treatment using ddI or ddC in patients with advanced HIV infection. Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 11, 161-169. Garre, F., Zwinderman, A., Geskus, R., and Sijpkens, Y. (2008). A joint latent class changepoint model to improve the prediction of time to graft failure. Journal of the Royal Statistical Society, Series A 171, 299-308. Pencina, M., D'Agostino, Sr., R., D'Agostino, Jr., R., and Vasan, R. (2008). Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond. Statistics in Medicine 27, 157-172. Wulfsohn, M. and Tsiatis, A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics 53, 330-339. Fitzmaurice, G., Laird, N., and Ware, J. (2004). Applied Longitudinal Data. Hoboken , New Jersey : Wiley. Proust-Lima, C. and Taylor, J. (2009). Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach. Biostatistics 10, 535-549. Schemper, M. and Henderson, R. (2000). Predictive accuracy and explained variation in Cox regression. Biometrics 56, 249-255. Ye, W., Lin, X., and Taylor, J. (2008). A penalized likelihood approach to joint modeling of longitudinal measurements and time-to-event data. Statistics and Its Interface 1, 33-45. Rizopoulos, D. (2010). JM: An R package for the joint modelling of longitudinal and time-to-event data. Journal of Statistical Software 35 (9), 1-33. Song, X., Davidian, M., and Tsiatis, A. (2002). A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 58, 742-753. Yu, M., Law, N., Taylor, J., and Sandler, H. (2004). Joint longitudinal-survival-cure models and their application to prostate cancer. Statistica Sinica 14, 835-832. Cox, D. and Hinkley, D. (1974). Theoretical Statistics. London : Chapman & Hall. Yu, M., Taylor, J., and Sandler, H. (2008). Individualized prediction in prostate cancer studies using a joint longitudinal-survival-cure model. Journal of the American Statistical Association 103, 178-187. Harrell, F., Kerry, L., and Mark, D. (1996). Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 15, 361-387. Faucett, C. and Thomas, D. (1996). Simultaneously modelling censored survival data and repeatedly measured covariates: A Gibbs sampling approach. Statistics in Medicine 15, 1663-1685. Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York : Springer-Verlag. 1994; 330 2002; 58 2010; 35 2011 1974 1982; 247 2004 2000; 1 2008; 103 2005; 61 2002 2008; 1 2008; 95 1996; 15 2005; 23 2005; 24 1996; 11 2009; 10 2000 2000; 56 1997; 53 2009; 71 2004; 14 2008; 27 2005; 92 2008; 64 2007; 63 2008; 171 Brown (10.1111/j.1541-0420.2010.01546.x-BIB3|cit3) 2005; 61 Wulfsohn (10.1111/j.1541-0420.2010.01546.x-BIB28|cit28) 1997; 53 Schemper (10.1111/j.1541-0420.2010.01546.x-BIB22|cit22) 2000; 56 Faucett (10.1111/j.1541-0420.2010.01546.x-BIB7|cit7) 1996; 15 Yu (10.1111/j.1541-0420.2010.01546.x-BIB31|cit31) 2008; 103 Harrell (10.1111/j.1541-0420.2010.01546.x-BIB11|cit11) 1982; 247 Abrams (10.1111/j.1541-0420.2010.01546.x-BIB1|cit1) 1994; 330 Henderson (10.1111/j.1541-0420.2010.01546.x-BIB14|cit14) 2000; 1 Rizopoulos (10.1111/j.1541-0420.2010.01546.x-BIB18|cit18) 2010; 35 Elashoff (10.1111/j.1541-0420.2010.01546.x-BIB6|cit6) 2008; 64 Kalbfleisch (10.1111/j.1541-0420.2010.01546.x-BIB15|cit15) 2002 Antolini (10.1111/j.1541-0420.2010.01546.x-BIB2|cit2) 2005; 24 Proust-Lima (10.1111/j.1541-0420.2010.01546.x-BIB17|cit17) 2009; 10 Tseng (10.1111/j.1541-0420.2010.01546.x-BIB25|cit25) 2005; 92 Fitzmaurice (10.1111/j.1541-0420.2010.01546.x-BIB8|cit8) 2004 Ding (10.1111/j.1541-0420.2010.01546.x-BIB5|cit5) 2008; 64 Taylor (10.1111/j.1541-0420.2010.01546.x-BIB24|cit24) 2005; 23 Goldman (10.1111/j.1541-0420.2010.01546.x-BIB10|cit10) 1996; 11 Heagerty (10.1111/j.1541-0420.2010.01546.x-BIB13|cit13) 2005; 61 Rizopoulos (10.1111/j.1541-0420.2010.01546.x-BIB19|cit19) 2011 Harrell (10.1111/j.1541-0420.2010.01546.x-BIB12|cit12) 1996; 15 Zheng (10.1111/j.1541-0420.2010.01546.x-BIB32|cit32) 2007; 63 Verbeke (10.1111/j.1541-0420.2010.01546.x-BIB27|cit27) 2000 Song (10.1111/j.1541-0420.2010.01546.x-BIB23|cit23) 2002; 58 Garre (10.1111/j.1541-0420.2010.01546.x-BIB9|cit9) 2008; 171 Tsiatis (10.1111/j.1541-0420.2010.01546.x-BIB26|cit26) 2004; 14 Cox (10.1111/j.1541-0420.2010.01546.x-BIB4|cit4) 1974 Pencina (10.1111/j.1541-0420.2010.01546.x-BIB16|cit16) 2008; 27 Rizopoulos (10.1111/j.1541-0420.2010.01546.x-BIB20|cit20) 2009; 71 Rizopoulos (10.1111/j.1541-0420.2010.01546.x-BIB21|cit21) 2008; 95 Ye (10.1111/j.1541-0420.2010.01546.x-BIB29|cit29) 2008; 1 Yu (10.1111/j.1541-0420.2010.01546.x-BIB30|cit30) 2004; 14 |
| References_xml | – reference: Rizopoulos, D., Verbeke, G., and Lesaffre, E. (2009). Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society, Series B 71, 637-654. – reference: Antolini, L., Boracchi, P., and Biganzoli, E. (2005). A time-dependent discrimination index for survival data. Statistics in Medicine 24, 3927-3944. – reference: Pencina, M., D'Agostino, Sr., R., D'Agostino, Jr., R., and Vasan, R. (2008). Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond. Statistics in Medicine 27, 157-172. – reference: Fitzmaurice, G., Laird, N., and Ware, J. (2004). Applied Longitudinal Data. Hoboken , New Jersey : Wiley. – reference: Tseng, Y.-K., Hsieh, F., and Wang, J.-L. (2005). Joint modelling of accelerated failure time and longitudinal data. Biometrika 92, 587-603. – reference: Wulfsohn, M. and Tsiatis, A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics 53, 330-339. – reference: Rizopoulos, D., Verbeke, G., and Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika 95, 63-74. – reference: Schemper, M. and Henderson, R. (2000). Predictive accuracy and explained variation in Cox regression. Biometrics 56, 249-255. – reference: Garre, F., Zwinderman, A., Geskus, R., and Sijpkens, Y. (2008). A joint latent class changepoint model to improve the prediction of time to graft failure. Journal of the Royal Statistical Society, Series A 171, 299-308. – reference: Brown, E., Ibrahim, J., and DeGruttola, V. (2005). A flexible B-spline model for multiple longitudinal biomarkers and survival. Biometrics 61, 64-73. – reference: Ding, J. and Wang, J.-L. (2008). Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics 64, 546-556. – reference: Rizopoulos, D. (2010). JM: An R package for the joint modelling of longitudinal and time-to-event data. Journal of Statistical Software 35 (9), 1-33. – reference: Yu, M., Law, N., Taylor, J., and Sandler, H. (2004). Joint longitudinal-survival-cure models and their application to prostate cancer. Statistica Sinica 14, 835-832. – reference: Elashoff, R., Li, G., and Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics 64, 762-771. – reference: Yu, M., Taylor, J., and Sandler, H. (2008). Individualized prediction in prostate cancer studies using a joint longitudinal-survival-cure model. Journal of the American Statistical Association 103, 178-187. – reference: Harrell, F., Callif, R., Pryor, D., Lee, K., and Rosati, R. (1982). Evaluating the yield of medical tests. Journal of the American Medical Association 247, 2543-2546. – reference: Kalbfleisch, J. and Prentice, R. (2002). The Statistical Analysis of Failure Time Data, 2nd edition. New York : Wiley. – reference: Faucett, C. and Thomas, D. (1996). Simultaneously modelling censored survival data and repeatedly measured covariates: A Gibbs sampling approach. Statistics in Medicine 15, 1663-1685. – reference: Proust-Lima, C. and Taylor, J. (2009). Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach. Biostatistics 10, 535-549. – reference: Tsiatis, A. and Davidian, M. (2004). Joint modeling of longitudinal and time-to-event data: An overview. Statistica Sinica 14, 809-834. – reference: Taylor, J., Yu, M., and Sandler, H. (2005). Individualized predictions of disease progression following radiation therapy for prostate cancer. Journal of Clinical Oncology 23, 816-825. – reference: Zheng, Y. and Heagerty, P. (2007). Prospective accuracy for longitudinal markers. Biometrics 63, 332-341. – reference: Abrams, D., Goldman, A., Launer, C., Korvick, A., Neaton, J., Crane, L., Grodesky, M., Wakefield, S., Muth, K., Kornegay, S., Cohn, D., Harris, A., Luskin-Hawk, R., Markowitz, N., Sampson, J., Thompson, M., Deyton, L. and the Terry Beirn Community Programs for Clinical Research on AIDS. (1994). Comparative trial of didanosine and zalcitabine in patients with human immunodeficiency virus infection who are intolerant of or have failed zidovudine therapy. New England Journal of Medicine 330, 657-662. – reference: Ye, W., Lin, X., and Taylor, J. (2008). A penalized likelihood approach to joint modeling of longitudinal measurements and time-to-event data. Statistics and Its Interface 1, 33-45. – reference: Harrell, F., Kerry, L., and Mark, D. (1996). Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 15, 361-387. – reference: Henderson, R., Diggle, P., and Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics 1, 465-480. – reference: Goldman, A., Carlin, B., Crane, L., Launer, C., Korvick, J., Deyton, L., and Abrams, D. (1996). Response of CD4+ and clinical consequences to treatment using ddI or ddC in patients with advanced HIV infection. Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 11, 161-169. – reference: Song, X., Davidian, M., and Tsiatis, A. (2002). A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 58, 742-753. – reference: Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York : Springer-Verlag. – reference: Heagerty, P. and Zheng, Y. (2005). Survival model predictive accuracy and ROC curves. Biometrics 61, 92-105. – reference: Cox, D. and Hinkley, D. (1974). Theoretical Statistics. London : Chapman & Hall. – year: 2011 – volume: 247 start-page: 2543 year: 1982 end-page: 2546 article-title: Evaluating the yield of medical tests publication-title: Journal of the American Medical Association – volume: 35 start-page: 1 issue: 9 year: 2010 end-page: 33 article-title: : An package for the joint modelling of longitudinal and time‐to‐event data publication-title: Journal of Statistical Software – volume: 61 start-page: 64 year: 2005 end-page: 73 article-title: A flexible B‐spline model for multiple longitudinal biomarkers and survival publication-title: Biometrics – volume: 64 start-page: 546 year: 2008 end-page: 556 article-title: Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data publication-title: Biometrics – volume: 61 start-page: 92 year: 2005 end-page: 105 article-title: Survival model predictive accuracy and ROC curves publication-title: Biometrics – volume: 92 start-page: 587 year: 2005 end-page: 603 article-title: Joint modelling of accelerated failure time and longitudinal data publication-title: Biometrika – volume: 23 start-page: 816 year: 2005 end-page: 825 article-title: Individualized predictions of disease progression following radiation therapy for prostate cancer publication-title: Journal of Clinical Oncology – year: 2000 – volume: 11 start-page: 161 year: 1996 end-page: 169 article-title: Response of CD4+ and clinical consequences to treatment using ddI or ddC in patients with advanced HIV infection publication-title: Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology – volume: 10 start-page: 535 year: 2009 end-page: 549 article-title: Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach publication-title: Biostatistics – volume: 1 start-page: 33 year: 2008 end-page: 45 article-title: A penalized likelihood approach to joint modeling of longitudinal measurements and time‐to‐event data publication-title: Statistics and Its Interface – volume: 71 start-page: 637 year: 2009 end-page: 654 article-title: Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data publication-title: Journal of the Royal Statistical Society, Series B – volume: 330 start-page: 657 year: 1994 end-page: 662 article-title: Comparative trial of didanosine and zalcitabine in patients with human immunodeficiency virus infection who are intolerant of or have failed zidovudine therapy publication-title: New England Journal of Medicine – volume: 14 start-page: 809 year: 2004 end-page: 834 article-title: Joint modeling of longitudinal and time‐to‐event data: An overview publication-title: Statistica Sinica – volume: 24 start-page: 3927 year: 2005 end-page: 3944 article-title: A time‐dependent discrimination index for survival data publication-title: Statistics in Medicine – volume: 171 start-page: 299 year: 2008 end-page: 308 article-title: A joint latent class changepoint model to improve the prediction of time to graft failure publication-title: Journal of the Royal Statistical Society, Series A – volume: 15 start-page: 361 year: 1996 end-page: 387 article-title: Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors publication-title: Statistics in Medicine – volume: 1 start-page: 465 year: 2000 end-page: 480 article-title: Joint modelling of longitudinal measurements and event time data publication-title: Biostatistics – volume: 14 start-page: 835 year: 2004 end-page: 832 article-title: Joint longitudinal‐survival‐cure models and their application to prostate cancer publication-title: Statistica Sinica – volume: 27 start-page: 157 year: 2008 end-page: 172 article-title: Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond publication-title: Statistics in Medicine – volume: 95 start-page: 63 year: 2008 end-page: 74 article-title: Shared parameter models under random effects misspecification publication-title: Biometrika – volume: 58 start-page: 742 year: 2002 end-page: 753 article-title: A semiparametric likelihood approach to joint modeling of longitudinal and time‐to‐event data publication-title: Biometrics – volume: 64 start-page: 762 year: 2008 end-page: 771 article-title: A joint model for longitudinal measurements and survival data in the presence of multiple failure types publication-title: Biometrics – year: 2002 – year: 2004 – year: 1974 – volume: 103 start-page: 178 year: 2008 end-page: 187 article-title: Individualized prediction in prostate cancer studies using a joint longitudinal‐survival‐cure model publication-title: Journal of the American Statistical Association – volume: 15 start-page: 1663 year: 1996 end-page: 1685 article-title: Simultaneously modelling censored survival data and repeatedly measured 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| Snippet | In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of... Summary In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event... |
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| SubjectTerms | Accuracy Area under the curve Bayes estimators BIOMETRIC METHODOLOGY Biometrics biometry Biometry - methods CD4 Lymphocyte Count CD4-Positive T-Lymphocytes - pathology Data analysis data collection Datasets Discrimination Estimate reliability Estimators HIV Infections - blood HIV Infections - mortality Human immunodeficiency virus Humans Induced substructures Longitudinal data Longitudinal Studies Maximum likelihood estimation Modeling patients prediction Probability ROC methodology Shared parameter model Standard error Survival Analysis Time Time series Time-dependent covariates |
| Title | Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time‐to‐Event Data |
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