Consistent estimation of the expected Brier score in general survival models with right-censored event times.
In survival analysis with censored data the mean squared error of prediction can be estimated by weighted averages of time-dependent residuals. Graf et al. (1999) suggested a robust weighting scheme based on the assumption that the censoring mechanism is independent of the covariates. We show consistency of the estimator. Furthermore, we show that a modified version of this estimator is consistent even when censoring and event times are only conditionally independent given the covariates. The modified estimators are derived on the basis of regression models for the censoring distribution. A simulation study and a real data example illustrate the results.
Gerds
Thomas A
TA
Institute of Medical Biometry and Medical Informatics, University of Freiburg, Stefan-Meier-Strasse 26, D-79104 Freiburg, Germany. gerds@fdm.uni-freiburg.de
Schumacher
Martin
M
D000465:Algorithms; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D018849:Controlled Clinical Trials as Topic / Q000379:methods*; D003627:Data Interpretation, Statistical; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods*; D012307:Risk Factors; D016019:Survival Analysis; D015996:Survival Rate