A unified inference procedure for a class of measures to assess improvement in risk prediction systems with survival data

Abstract

Risk prediction procedures can be quite useful for the patient's treatment selection, prevention strategy, or disease management in evidence-based medicine. Often, potentially important new predictors are available in addition to the conventional markers. The question is how to quantify the improvement from the new markers for prediction of the patient's risk in order to aid cost-benefit decisions. The standard method, using the area under the receiver operating characteristic curve, to measure the added value may not be sensitive enough to capture incremental improvements from the new markers. Recently, some novel alternatives to area under the receiver operating characteristic curve, such as integrated discrimination improvement and net reclassification improvement, were proposed. In this paper, we consider a class of measures for evaluating the incremental values of new markers, which includes the preceding two as special cases. We present a unified procedure for making inferences about measures in the class with censored event time data. The large sample properties of our procedures are theoretically justified. We illustrate the new proposal with data from a cancer study to evaluate a new gene score for prediction of the patient's survival.