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Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. (English) Zbl 1226.62124

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. 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)

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[1] Abrams, 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 pp 657– (1994) · doi:10.1056/NEJM199403103301001
[2] Antolini, A time-dependent discrimination index for survival data, Statistics in Medicine 24 pp 3927– (2005) · doi:10.1002/sim.2427
[3] Brown, A flexible B-spline model for multiple longitudinal biomarkers and survival, Biometrics 61 pp 64– (2005) · Zbl 1077.62102 · doi:10.1111/j.0006-341X.2005.030929.x
[4] Cox, Theoretical Statistics (1974) · doi:10.1007/978-1-4899-2887-0
[5] Ding, Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data, Biometrics 64 pp 546– (2008) · Zbl 1137.62075 · doi:10.1111/j.1541-0420.2007.00896.x
[6] Elashoff, A joint model for longitudinal measurements and survival data in the presence of multiple failure types, Biometrics 64 pp 762– (2008) · Zbl 1170.62067 · doi:10.1111/j.1541-0420.2007.00952.x
[7] Faucett, Simultaneously modelling censored survival data and repeatedly measured covariates: A Gibbs sampling approach, Statistics in Medicine 15 pp 1663– (1996) · doi:10.1002/(SICI)1097-0258(19960815)15:15<1663::AID-SIM294>3.0.CO;2-1
[8] Fitzmaurice, Applied Longitudinal Data (2004)
[9] Garre, A joint latent class changepoint model to improve the prediction of time to graft failure, Journal of the Royal Statistical Society, Series A 171 pp 299– (2008)
[10] Goldman, 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 pp 161– (1996) · doi:10.1097/00042560-199602010-00007
[11] Harrell, Evaluating the yield of medical tests, Journal of the American Medical Association 247 pp 2543– (1982) · doi:10.1001/jama.247.18.2543
[12] Harrell, Multivariable prognostic models: Issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors, Statistics in Medicine 15 pp 361– (1996) · doi:10.1002/(SICI)1097-0258(19960229)15:4<361::AID-SIM168>3.0.CO;2-4
[13] Heagerty, Survival model predictive accuracy and ROC curves, Biometrics 61 pp 92– (2005) · Zbl 1077.62077 · doi:10.1111/j.0006-341X.2005.030814.x
[14] Henderson, Joint modelling of longitudinal measurements and event time data, Biostatistics 1 pp 465– (2000) · Zbl 1089.62519 · doi:10.1093/biostatistics/1.4.465
[15] Kalbfleisch, The Statistical Analysis of Failure Time Data (2002) · Zbl 1012.62104 · doi:10.1002/9781118032985
[16] Pencina, Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond, Statistics in Medicine 27 pp 157– (2008) · doi:10.1002/sim.2929
[17] Proust-Lima, Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach, Biostatistics 10 pp 535– (2009) · doi:10.1093/biostatistics/kxp009
[18] Rizopoulos, JM: An R package for the joint modelling of longitudinal and time-to-event data, Journal of Statistical Software 35 (9) pp 1– (2010) · doi:10.18637/jss.v035.i09
[19] Rizopoulos, To appear in Statistics in Medicine (2011)
[20] Rizopoulos, Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data, Journal of the Royal Statistical Society, Series B 71 pp 637– (2009) · Zbl 1250.62049 · doi:10.1111/j.1467-9868.2008.00704.x
[21] Rizopoulos, Shared parameter models under random effects misspecification, Biometrika 95 pp 63– (2008) · Zbl 1437.62592 · doi:10.1093/biomet/asm087
[22] Schemper, Predictive accuracy and explained variation in Cox regression, Biometrics 56 pp 249– (2000) · Zbl 1060.62663 · doi:10.1111/j.0006-341X.2000.00249.x
[23] Song, A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data, Biometrics 58 pp 742– (2002) · Zbl 1210.62132 · doi:10.1111/j.0006-341X.2002.00742.x
[24] Taylor, Individualized predictions of disease progression following radiation therapy for prostate cancer, Journal of Clinical Oncology 23 pp 816– (2005) · doi:10.1200/JCO.2005.12.156
[25] Tseng, Joint modelling of accelerated failure time and longitudinal data, Biometrika 92 pp 587– (2005) · Zbl 1152.62380 · doi:10.1093/biomet/92.3.587
[26] Tsiatis, Joint modeling of longitudinal and time-to-event data: An overview, Statistica Sinica 14 pp 809– (2004) · Zbl 1073.62087
[27] Verbeke, Linear Mixed Models for Longitudinal Data (2000)
[28] Wulfsohn, A joint model for survival and longitudinal data measured with error, Biometrics 53 pp 330– (1997) · Zbl 0874.62140 · doi:10.2307/2533118
[29] Ye, A penalized likelihood approach to joint modeling of longitudinal measurements and time-to-event data, Statistics and Its Interface 1 pp 33– (2008) · Zbl 1230.62132 · doi:10.4310/SII.2008.v1.n1.a4
[30] Yu, Joint longitudinal-survival-cure models and their application to prostate cancer, Statistica Sinica 14 pp 835– (2004) · Zbl 1073.62111
[31] Yu, Individualized prediction in prostate cancer studies using a joint longitudinal-survival-cure model, Journal of the American Statistical Association 103 pp 178– (2008) · Zbl 1469.62383 · doi:10.1198/016214507000000400
[32] Zheng, Prospective accuracy for longitudinal markers, Biometrics 63 pp 332– (2007) · Zbl 1140.62086 · doi:10.1111/j.1541-0420.2006.00726.x
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