A Robust Alternative to the Schemper-Henderson Estimator of Prediction Error

In clinical applications, the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models. Different approaches to evaluate the predictive performance of survival models have been suggested in the literature. In this article, we analyze the properties of the estimator of prediction error developed by Schemper and Henderson (2000, Biometrics 56, 249-255), which quantifies the absolute distance between predicted and observed survival functions. We provide a formal proof that the estimator proposed by Schemper and Henderson is not robust against misspecification of the survival model, that is, the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly. To remedy this problem, we construct a new estimator of the absolute distance between predicted and observed survival functions. We show that this modified Schemper-Henderson estimator is robust against model misspecification, allowing its practical application to a wide class of survival models. The properties of the Schemper-Henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets.