The use of ROC for defining the validity of the prognostic index in censored data

The validity of a diagnostic marker can be summarised by using statistical measures either for the goodness of the fit like the deviance, measures of the explained variation like R2 or the misclassification rate. Other intuitive measures are sensitivity and specificity in the case of binary response. In the absence of censored data the calculation of these measures is widely used. In the presence of censoring the estimation of time-dependent sensitivity and specificity is not well known. In this article we propose a new method for calculating ROC curves with censored data using the observed number of events and calculating the additional number of expected events for censored observations. The new method is illustrated with data for predicting mortality in patients surviving a myocardial infarction.