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Keywords:

  • Brier score;
  • IPCW;
  • Prediction error;
  • Quadratic loss

Abstract

Prognostic models for time-to-event data play a prominent role in therapy assignment, risk stratification and inter-hospital quality assurance. The assessment of their prognostic value is vital not only for responsible resource allocation, but also for their widespread acceptance. The additional presence of competing risks to the event of interest requires proper handling not only on the model building side, but also during assessment. Research into methods for the evaluation of the prognostic potential of models accounting for competing risks is still needed, as most proposed methods measure either their discrimination or calibration, but do not examine both simultaneously. We adapt the prediction error proposal of Graf et al. (Statistics in Medicine 1999, 18, 2529–2545) and Gerds and Schumacher (Biometrical Journal 2006, 48, 1029–1040) to handle models with competing risks, i.e. more than one possible event type, and introduce a consistent estimator. A simulation study investigating the behaviour of the estimator in small sample size situations and for different levels of censoring together with a real data application follows.