title: Joint modelling of repeated measurement and time-to-event data: an introductory tutorial.
abstract: BACKGROUND
  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.
authors.affiliation: CHICAS, Lancaster Medical School, Lancaster University, Lancaster, UK, Vascular Research Group, Manchester Academic Health Sciences Centre, University of Manchester, Salford Royal NHS Foundation Trust, UK and Institute of Infection and Global Health, University of Liverpool, Liverpool, UK o.asar@lancaster.ac.uk.
authors.forename: Özgür
authors.initials: Ö
authors.lastname: Asar
authors.affiliation: CHICAS, Lancaster Medical School, Lancaster University, Lancaster, UK, Vascular Research Group, Manchester Academic Health Sciences Centre, University of Manchester, Salford Royal NHS Foundation Trust, UK and Institute of Infection and Global Health, University of Liverpool, Liverpool, UK.
authors.forename: James
authors.initials: J
authors.lastname: Ritchie
authors.affiliation: CHICAS, Lancaster Medical School, Lancaster University, Lancaster, UK, Vascular Research Group, Manchester Academic Health Sciences Centre, University of Manchester, Salford Royal NHS Foundation Trust, UK and Institute of Infection and Global Health, University of Liverpool, Liverpool, UK.
authors.forename: Philip A
authors.initials: PA
authors.lastname: Kalra
authors.affiliation: CHICAS, Lancaster Medical School, Lancaster University, Lancaster, UK, Vascular Research Group, Manchester Academic Health Sciences Centre, University of Manchester, Salford Royal NHS Foundation Trust, UK and Institute of Infection and Global Health, University of Liverpool, Liverpool, UK CHICAS, Lancaster Medical School, Lancaster University, Lancaster, UK, Vascular Research Group, Manchester Academic Health Sciences Centre, University of Manchester, Salford Royal NHS Foundation Trust, UK and Institute of Infection and Global Health, University of Liverpool, Liverpool, UK.
authors.forename: Peter J
authors.initials: PJ
authors.lastname: Diggle
mesh_terms: D005919:Glomerular Filtration Rate; D006801:Humans; D007676:Kidney Failure, Chronic / Q000401:mortality / Q000628:therapy; D008137:Longitudinal Studies; D015233:Models, Statistical; D016016:Proportional Hazards Models; D017582:Renal Replacement Therapy / Q000379:methods / Q000401:mortality; D012107:Research Design; D016019:Survival Analysis; D013997:Time Factors
keywords: Chronic kidney disease; cohort study; epidemiology; joint modelling of longitudinal and survival data; measurement error; medical statistics; statistical software