Assessing quantile prediction with censored quantile regression models

An important goal of censored quantile regression is to provide reliable predictions of survival quantiles, which are often reported in practice to offer robust and comprehensive biomedical summaries. However, formal methods for evaluating and comparing working quantile regression models in terms of their performance in predicting survival quantiles have been lacking, especially when the working models are subject to model mis-specification. In this article, we proposes a sensible and rigorous framework to fill in this gap. We introduce and justify a predictive performance measure defined based on the check loss function. We derive estimators of the proposed predictive performance measure and study their distributional properties and the corresponding inference procedures. More importantly, we develop model comparison procedures that enable thorough evaluations of model predictive performance among nested or non-nested models. Our proposals properly accommodate random censoring to the survival outcome and the realistic complication of model mis-specification, and thus are generally applicable. Extensive simulations and a real data example demonstrate satisfactory performances of the proposed methods in real life settings.