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Concordance probability and discriminatory power in proportional hazards regression


  • Mithat Gonen
  • Glenn Heller


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. Copyright 2005, Oxford University Press.

Suggested Citation

  • Mithat Gonen & Glenn Heller, 2005. "Concordance probability and discriminatory power in proportional hazards regression," Biometrika, Biometrika Trust, vol. 92(4), pages 965-970, December.
  • Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:965-970

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    Cited by:

    1. Liu Xinhua & Jin Zhezhen, 2009. "A Non-Parametric Approach to Scale Reduction for Uni-Dimensional Screening Scales," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-22, January.
    2. Verwaeren, Jan & Waegeman, Willem & De Baets, Bernard, 2012. "Learning partial ordinal class memberships with kernel-based proportional odds models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 928-942.
    3. Glenn Heller & Qianxing Mo, 2016. "Estimating the concordance probability in a survival analysis with a discrete number of risk groups," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 263-279, April.
    4. repec:eee:joecas:v:13:y:2016:i:c:p:100-113 is not listed on IDEAS
    5. repec:eee:ecosta:v:7:y:2018:i:c:p:153-164 is not listed on IDEAS
    6. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0766-7 is not listed on IDEAS
    7. repec:spr:stabio:v:10:y:2018:i:3:d:10.1007_s12561-018-9216-5 is not listed on IDEAS
    8. Wolf, Petra & Schmidt, Georg & Ulm, Kurt, 2011. "The use of ROC for defining the validity of the prognostic index in censored data," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 783-791, July.
    9. repec:spr:qualqt:v:52:y:2018:i:2:d:10.1007_s11135-018-0697-6 is not listed on IDEAS

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