Concordance for prognostic models with competing risks.
The concordance probability is a widely used measure to assess discrimination of prognostic models with binary and survival endpoints. We formally define the concordance probability for a prognostic model of the absolute risk of an event of interest in the presence of competing risks and relate it to recently proposed time-dependent area under the receiver operating characteristic curve measures. For right-censored data, we investigate inverse probability of censoring weighted (IPCW) estimates of a truncated concordance index based on a working model for the censoring distribution. We demonstrate consistency and asymptotic normality of the IPCW estimate if the working model is correctly specified and derive an explicit formula for the asymptotic variance under independent censoring. The small sample properties of the estimator are assessed in a simulation study also against misspecification of the working model. We further illustrate the methods by computing the concordance probability for a prognostic model of coronary heart disease (CHD) events in the presence of the competing risk of non-CHD death.
Oxford University Clinical Research Unit, Wellcome Trust Major Overseas Programme, Ho Chi Minh City, Viet Nam and Centre for Tropical Medicine, Nuffield Department of Medicine, University of Oxford, Oxford, OX3 7FZ, UK mwolbers@oucru.org.
Marcel
M
Wolbers
Université Bordeaux Segalen, ISPED, INSERM U897, F-33000 Bordeaux, France.
Paul
P
Blanche
Basel Institute for Clinical Epidemiology and Biostatistics, University Hospital Basel, 4031 Basel, Switzerland.
Michael T
MT
Koller
Erasmus Medical Center, 3015 Rotterdam, The Netherlands.
Jacqueline C M
JC
Witteman
Department of Biostatistics, University of Copenhagen, 1014 Copenhagen K, Denmark.
Thomas A
TA
Gerds
D003327:Coronary Disease / Q000453:epidemiology; D006801:Humans; D015233:Models, Statistical; D011336:Probability; D011379:Prognosis; D012372:ROC Curve
C index; Competing risks; Concordance probability; Coronary heart disease; Prognostic models; Time-dependent AUC