Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks

Stat Med. 2013 Dec 30;32(30):5381-97. doi: 10.1002/sim.5958. Epub 2013 Sep 12.


The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable.

Keywords: AUC; competing risks; discrimination; inverse probability of censoring weighting; prognosis; survival analysis.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Aged
  • Aged, 80 and over
  • Area Under Curve*
  • Biomarkers / analysis*
  • Computer Simulation
  • Confidence Intervals*
  • Data Interpretation, Statistical*
  • Dementia / diagnosis
  • France
  • Humans
  • Predictive Value of Tests*
  • Psychological Tests
  • ROC Curve*


  • Biomarkers