On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data
Hajime Unoa b c✉, Tianxi Caic, Michael J. Pencinad, Ralph B. D’Agostinoe, L. J. Weic
- aDepartment of Biostatistics and Computational Biology, Dana Farber Cancer Institute, Boston, MA, USA. huno@jimmy.harvard.edu
- bDepartment of Biostatistics and Computational Biology, Dana Farber Cancer Institute, Boston, MA, U.S.A
- cDepartment of Biostatistics, Harvard University, Boston, MA, U.S.A
- dDepartment of Biostatistics, Boston University, Boston, MA, U.S.A
- eDepartment of Mathematics and Statistics, Boston University, Boston, MA, U.S.A
- ✉Corresponding author
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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.