Joint modelling of repeated measurement and time-to-event data: an introductory tutorial.

BACKGOUND The term 'joint modelling' is used in the statistical literature to refer to methods for simultaneously analysing longitudinal measurement outcomes, also called repeated measurement data, and time-to-event outcomes, also called survival data. A typical example from nephrology is a study in which the data from each participant consist of repeated estimated glomerular filtration rate (eGFR) measurements and time to initiation of renal replacement therapy (RRT). Joint models typically combine linear mixed effects models for repeated measurements and Cox models for censored survival outcomes. Our aim in this paper is to present an introductory tutorial on joint modelling methods, with a case study in nephrology. METHODS We describe the development of the joint modelling framework and compare the results with those obtained by the more widely used approaches of conducting separate analyses of the repeated measurements and survival times based on a linear mixed effects model and a Cox model, respectively. Our case study concerns a data set from the Chronic Renal Insufficiency Standards Implementation Study (CRISIS). We also provide details of our open-source software implementation to allow others to replicate and/or modify our analysis. RESULTS The results for the conventional linear mixed effects model and the longitudinal component of the joint models were found to be similar. However, there were considerable differences between the results for the Cox model with time-varying covariate and the time-to-event component of the joint model. For example, the relationship between kidney function as measured by eGFR and the hazard for initiation of RRT was significantly underestimated by the Cox model that treats eGFR as a time-varying covariate, because the Cox model does not take measurement error in eGFR into account. CONCLUSIONS Joint models should be preferred for simultaneous analyses of repeated measurement and survival data, especially when the former is measured with error and the association between the underlying error-free measurement process and the hazard for survival is of scientific interest.

[1]  Joseph G Ibrahim,et al.  Basic concepts and methods for joint models of longitudinal and survival data. , 2010, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[2]  A. Levey,et al.  A More Accurate Method To Estimate Glomerular Filtration Rate from Serum Creatinine: A New Prediction Equation , 1999, Annals of Internal Medicine.

[3]  C. Kendziorski,et al.  The efficiency of pooling mRNA in microarray experiments. , 2003, Biostatistics.

[4]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[5]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[6]  Maral Saadati,et al.  Joint Models for Longitudinal and Time-to-Event Data with Applications in R. Dimitris Rizopoulos (2012). Boca Raton: Chapman & Hall/CRC Texts in Statistical Science Series. 261 pages, ISBN: 978-1439872864. , 2013 .

[7]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[8]  D.,et al.  Regression Models and Life-Tables , 2022 .

[9]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[10]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[11]  Y. Pawitan In all likelihood : statistical modelling and inference using likelihood , 2002 .

[12]  Cécile Proust-Lima,et al.  Joint latent class models for longitudinal and time-to-event data: A review , 2014, Statistical methods in medical research.

[13]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[14]  Dimitris Rizopoulos,et al.  JM: An R package for the joint modelling of longitudinal and time-to-event data , 2010 .

[15]  Aeilko H. Zwinderman,et al.  A joint latent class changepoint model to improve the prediction of time to graft failure , 2007 .

[16]  D. Kleinbaum,et al.  Survival Analysis: A Self-Learning Text. , 1996 .

[17]  Bradley P Carlin,et al.  Separate and Joint Modeling of Longitudinal and Event Time Data Using Standard Computer Packages , 2004 .

[18]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[19]  Benoit Liquet,et al.  Estimation of extended mixed models using latent classes and latent processes: the R package lcmm , 2015, 1503.00890.

[20]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[21]  D. Rizopoulos,et al.  Impact of longitudinal exposure to mycophenolic acid on acute rejection in renal-transplant recipients using a joint modeling approach. , 2013, Pharmacological research.

[22]  Geert Molenberghs,et al.  Random Effects Models for Longitudinal Data , 2010 .

[23]  J. Ware,et al.  Applied Longitudinal Analysis , 2004 .

[24]  Eleni-Rosalina Andrinopoulou,et al.  An introduction to mixed models and joint modeling: analysis of valve function over time. , 2012, The Annals of thoracic surgery.

[25]  Geert Molenberghs,et al.  Missing Data in Clinical Studies , 2007 .

[26]  P. Diggle,et al.  Analysis of Longitudinal Data. , 1997 .

[27]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[28]  M. Wulfsohn,et al.  A joint model for survival and longitudinal data measured with error. , 1997, Biometrics.

[29]  J. New,et al.  Factors associated with kidney disease progression and mortality in a referred CKD population. , 2010, American journal of kidney diseases : the official journal of the National Kidney Foundation.

[30]  R. Kolamunnage-Dona,et al.  Joint modelling of longitudinal and competing risks data , 2008, Statistics in medicine.

[31]  F J Ingelfinger,et al.  International Journal of Epidemiology , 1973, The New England journal of medicine.

[32]  Wei Shen,et al.  Assessing model fit in joint models of longitudinal and survival data with applications to cancer clinical trials , 2014, Statistics in medicine.

[33]  Simon G Thompson,et al.  Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture , 2011, Biometrical journal. Biometrische Zeitschrift.

[34]  R. Prentice Covariate measurement errors and parameter estimation in a failure time regression model , 1982 .

[35]  Joseph G. Ibrahim,et al.  Missing data methods in longitudinal studies: a review , 2009 .

[36]  Peter J. Diggle,et al.  joineR: Joint modelling of repeated measurements and time-to-event data , 2012 .

[37]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[38]  Robin Henderson,et al.  Diagnostics for Joint Longitudinal and Dropout Time Modeling , 2003, Biometrics.

[39]  D. Rizopoulos,et al.  Local sensitivity to non-ignorability in joint models , 2014 .

[40]  R Henderson,et al.  Joint modelling of longitudinal measurements and event time data. , 2000, Biostatistics.

[41]  P. Grambsch,et al.  A Package for Survival Analysis in S , 1994 .

[42]  Amanda G Chetwynd,et al.  Joint modelling of repeated measurements and time‐to‐event outcomes: The fourth Armitage lecture , 2008, Statistics in medicine.

[43]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[44]  Dimitris Rizopoulos Event Time Event Time , 2012 .

[45]  Geert Molenberghs,et al.  Multiple‐Imputation‐Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes , 2010, Biometrics.

[46]  J. New,et al.  Serum phosphate and mortality in patients with chronic kidney disease. , 2010, Clinical journal of the American Society of Nephrology : CJASN.

[47]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.