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Keywords:

  • Discriminant analysis;
  • Nonparametric function estimation;
  • Prediction;
  • Receiver operating characteristic curve

Summary Quantitative procedures for evaluating added values from new markers over a conventional risk scoring system for predicting event rates at specific time points have been extensively studied. However, a single summary statistic, for example, the area under the receiver operating characteristic curve or its derivatives, may not provide a clear picture about the relationship between the conventional and the new risk scoring systems. When there are no censored event time observations in the data, two simple scatterplots with individual conventional and new scores for “cases” and “controls” provide valuable information regarding the overall and the subject-specific level incremental values from the new markers. Unfortunately, in the presence of censoring, it is not clear how to construct such plots. In this article, we propose a nonparametric estimation procedure for the distributions of the differences between two risk scores conditional on the conventional score. The resulting quantile curves of these differences over the subject-specific conventional score provide extra information about the overall added value from the new marker. They also help us to identify a subgroup of future subjects who need the new predictors, especially when there is no unified utility function available for cost–risk–benefit decision making. The procedure is illustrated with two data sets. The first is from a well-known Mayo Clinic primary biliary cirrhosis liver study. The second is from a recent breast cancer study on evaluating the added value from a gene score, which is relatively expensive to measure compared with the routinely used clinical biomarkers for predicting the patient’s survival after surgery.