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Biometrika 2005 92(4):965-970; doi:10.1093/biomet/92.4.965
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© 2005 Biometrika Trust

Miscellanea

Concordance probability and discriminatory power in proportional hazards regression

Mithat Gönen and Glenn Heller

Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, 307 East 63rd Street, New York, New York 10021, U.S.A. gonenm{at}mskcc.org, hellerg{at}mskcc.org

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytical expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer.

Key Words: Censored data; c-index; Cox model; Predictive accuracy

Received November 2004. Revised June 2005.


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