Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Joint modelling of repeated measurement and time-to-event data
T2 - an introductory tutorial
AU - Asar, Özgür
AU - Ritchie, James
AU - Kalra, Philip
AU - Diggle, Peter
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Chronic kidney disease
KW - cohort study
KW - epidemiology
KW - joint modelling of longitudinal and survival data
KW - measurement error
KW - medical statistics
KW - statistical software
U2 - 10.1093/ije/dyu262
DO - 10.1093/ije/dyu262
M3 - Journal article
C2 - 25604450
VL - 44
SP - 334
EP - 344
JO - International Journal of Epidemiology
JF - International Journal of Epidemiology
SN - 0300-5771
IS - 1
ER -