On the C-statistics for Evaluating Overall Adequacy of Risk Prediction Procedures with Censored Survival Data

By Hajime Uno, Tianxi Cai, Michael J. Pencina, R. D’Agostino, Lee-Jen Wei. Statistics in Medicine, 2011

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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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8d95e7c25c876d5f2d39db76a29d92a45a1527cf

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Citations in the corpus

External validation of prognostic models: what, why, how, when and where? (2020, methodology): “For Cox proportional hazards prediction models a time-toevent C-index such as Harrel’s C-index or Uno’s C-index can be computed [21, 25].”
Tumor aneuploidy correlates with markers of immune evasion and with reduced response to immunotherapy (2017, methodology): “In addition, for each model, we calculated the C-statistics (in cross validation: cvK = 4, Rep = 10) using the R package SurvC1 (56) (table S6).”
scikit-survival: A Library for Time-to-Event Analysis Built on Top of scikit-learn (2020, background): “Evaluation metrics range from simple rank correlation metrics (Harrell Pölsterl et al., 1996; Uno et al., 2011) to time-dependent versions of the well-known mean squared error (Graf et al., 1999) and receiver operating characteristic curve (Hung and Chiang, 2010; Uno et al., 2007).”
Developing clinical prediction models: a step-by-step guide (2024, neutral): “84 Calibration can be assessed for a fixed time point by comparing the average predicted survival from the model with the observed survival—ie, estimated while accounting for censorship; this can be obtained from a Kaplan-Meier curve by looking at the specific time point (calibration in the large…”