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Concordance probability and discriminatory power in proportional hazards regression

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  • Mithat Gonen
  • Glenn Heller

Abstract

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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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.965
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    Cited by:

    1. Schmid, Matthias & Tutz, Gerhard & Welchowski, Thomas, 2018. "Discrimination measures for discrete time-to-event predictions," Econometrics and Statistics, Elsevier, vol. 7(C), pages 153-164.
    2. Zhou, Fanyin & Fu, Lijun & Li, Zhiyong & Xu, Jiawei, 2022. "The recurrence of financial distress: A survival analysis," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1100-1115.
    3. Charmaine Pei Ling Lee & Hyungwon Choi & Khee Chee Soo & Min-Han Tan & Wen Yee Chay & Kee Seng Chia & Jenny Liu & Jingmei Li & Mikael Hartman, 2015. "Mammographic Breast Density and Common Genetic Variants in Breast Cancer Risk Prediction," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-16, September.
    4. 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.
    5. Lin Lu & Laurent Dercle & Binsheng Zhao & Lawrence H. Schwartz, 2021. "Deep learning for the prediction of early on-treatment response in metastatic colorectal cancer from serial medical imaging," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    6. Arazmuradov, Annageldy, 2016. "Assessing sovereign debt default by efficiency," The Journal of Economic Asymmetries, Elsevier, vol. 13(C), pages 100-113.
    7. Nuriye Sancar & Deniz Inan, 2018. "A novel method as a diagnostic tool for the detection of influential observations in the Cox proportional hazards model," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(2), pages 1253-1266, December.
    8. Kenichi Hayashi & Yasutaka Shimizu, 2018. "Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 546-567, December.
    9. Shengli An & Peter Zhang & Hong-Bin Fang, 2023. "Subgroup Identification in Survival Outcome Data Based on Concordance Probability Measurement," Mathematics, MDPI, vol. 11(13), pages 1-10, June.
    10. Patrick Ten Eyck & Joseph E. Cavanaugh, 2018. "Model selection criteria based on cross-validatory concordance statistics," Computational Statistics, Springer, vol. 33(2), pages 595-621, June.
    11. 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.
    12. 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.
    13. Sean M. Devlin & Mithat Gönen & Glenn Heller, 2020. "Measuring the temporal prognostic utility of a baseline risk score," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 856-871, October.
    14. Ruosha Li & Jing Ning & Ziding Feng, 2022. "Estimation and inference of predictive discrimination for survival outcome risk prediction models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 219-240, April.
    15. Yilong Zhang & Xiaoxia Han & Yongzhao Shao, 2021. "The ROC of Cox proportional hazards cure models with application in cancer studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 195-215, April.
    16. 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.
    17. Chrianna I Bharat & Kevin Murray & Edward Cripps & Melinda R Hodkiewicz, 2018. "Methods for displaying and calibration of Cox proportional hazards models," Journal of Risk and Reliability, , vol. 232(1), pages 105-115, February.

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