title: Time-dependent ROC curve analysis in medical research: current methods and applications.
abstract: ROC (receiver operating characteristic) curve analysis is well established for assessing how well a marker is capable of discriminating between individuals who experience disease onset and individuals who do not. The classical (standard) approach of ROC curve analysis considers event (disease) status and marker value for an individual as fixed over time, however in practice, both the disease status and marker value change over time. Individuals who are disease-free earlier may develop the disease later due to longer study follow-up, and also their marker value may change from baseline during follow-up. Thus, an ROC curve as a function of time is more appropriate. However, many researchers still use the standard ROC curve approach to determine the marker capability ignoring the time dependency of the disease status or the marker.
  
  
  
  We comprehensively review currently proposed methodologies of time-dependent ROC curves which use single or longitudinal marker measurements, aiming to provide clarity in each methodology, identify software tools to carry out such analysis in practice and illustrate several applications of the methodology. We have also extended some methods to incorporate a longitudinal marker and illustrated the methodologies using a sequential dataset from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver.
  
  
  
  From our methodological review, we have identified 18 estimation methods of time-dependent ROC curve analyses for censored event times and three other methods can only deal with non-censored event times. Despite the considerable numbers of estimation methods, applications of the methodology in clinical studies are still lacking.
  
  
  
  The value of time-dependent ROC curve methods has been re-established. We have illustrated the methods in practice using currently available software and made some recommendations for future research.
authors.affiliation: Department of Biostatistics, University of Liverpool, Liverpool, L69 3GL, UK. a.kamarudin@liverpool.ac.uk.
authors.forename: Adina Najwa
authors.initials: AN
authors.lastname: Kamarudin
authors.affiliation: Department of Biostatistics, University of Liverpool, Liverpool, L69 3GL, UK.
authors.forename: Trevor
authors.initials: T
authors.lastname: Cox
authors.affiliation: Department of Biostatistics, University of Liverpool, Liverpool, L69 3GL, UK.
authors.forename: Ruwanthi
authors.initials: R
authors.lastname: Kolamunnage-Dona
mesh_terms: D019540:Area Under Curve; D015415:Biomarkers / Q000032:analysis*; D003198:Computer Simulation; D006801:Humans; D008099:Liver / Q000473:pathology; D008105:Liver Cirrhosis, Biliary / Q000175:diagnosis*; D015233:Models, Statistical; D012372:ROC Curve
chemical_list: D015415:Biomarkers
keywords: Biomarker evaluation; Event-time; Longitudinal data; ROC curve; Software; Time-dependent AUC