On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data

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Abstract
For modern evidence‐based medicine, a well thought‐out risk scoring system for predicting the occurrence of a clinical event plays an important role in selecting prevention and treatment strategies. Such an index system is often established based on the subject's ‘baseline’ genetic or clinical markers via a working parametric or semi‐parametric model. To evaluate the adequacy of such a system, C‐statistics are routinely used in the medical literature to quantify the capacity of the estimated risk score in discriminating among subjects with different event times. The C‐statistic provides a global assessment of a fitted survival model for the continuous event time rather than focussing on the prediction of bit‐year survival for a fixed time. When the event time is possibly censored, however, the population parameters corresponding to the commonly used C‐statistics may depend on the study‐specific censoring distribution. In this article, we present a simple C‐statistic without this shortcoming. The new procedure consistently estimates a conventional concordance measure which is free of censoring. We provide a large sample approximation to the distribution of this estimator for making inferences about the concordance measure. Results from numerical studies suggest that the new procedure performs well in finite sample. Copyright © 2011 John Wiley & Sons, Ltd.