Net time-dependent ROC curves: a solution for evaluating the accuracy of a marker to predict disease-related mortality.

Developing prognostic markers of mortality for patients with chronic disease is important for identifying subjects at high risk of death and optimizing medical management. The usual approach in this regard is the use of time-dependent ROC curves, which are well adapted for censored data. Nevertheless, an important part of the mortality may not be due to the chronic disease, and it is often impossible to individually determine whether or not the deaths are related to the disease itself. In survival regression, one solution is to distinguish between the expected mortality of one general population (from life tables) and the excess mortality related to the disease, by using an additive relative survival model. In this paper, we propose a new estimator of time-dependent ROC curves, which includes this concept of net survival, in order to evaluate the capacity of a marker to predict disease-specific mortality. We performed simulations in order to validate this estimator. We also illustrate this method using two different applications: (i) predicting mortality related to primary biliary cirrhosis of the liver and (ii) predicting mortality related to kidney transplantation in end-stage renal disease patients. For each application, we evaluated a scoring system already established. The results demonstrate the utility of the proposed estimator of net time-dependent ROC curves.