Concordance probability and discriminatory power in proportional hazards regression

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.

[1]  F. Harrell,et al.  Evaluating the yield of medical tests. , 1982, JAMA.

[2]  S. Larson,et al.  Preoperative F-18 fluorodeoxyglucose-positron emission tomography maximal standardized uptake value predicts survival after lung cancer resection. , 2004, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[3]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[4]  G. Heller.  Incorporating Follow-up Time in M-Estimation for Survival Data , 2004, Lifetime data analysis.

[5]  M. Pencina,et al.  Overall C as a measure of discrimination in survival analysis: model specific population value and confidence interval estimation , 2004, Statistics in medicine.

[6]  R. H. Somers.  A Similarity between Goodman and Kruskal's Tau and Kendall's Tau, with a Partial Interpretation of the Latter , 1962 .

[7]  A. Tsiatis.  Estimating Regression Parameters Using Linear Rank Tests for Censored Data , 1990 .

[8]  F. Harrell,et al.  Regression modelling strategies for improved prognostic prediction. , 1984, Statistics in medicine.

[9]  Jean D. Gibbons,et al.  Concepts of Nonparametric Theory , 1981 .

[10]  J Stare,et al.  Explained variation in survival analysis. , 1996, Statistics in medicine.

[11]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[12]  Richard Simon,et al.  Explained Residual Variation, Explained Risk, and Goodness of Fit , 1991 .

[13]  James M. Robins,et al.  Semiparametric estimation of an accelerated failure time model with time-dependent covariates , 1992 .

[14]  G. Garrido Cantarero,et al.  [The area under the ROC curve]. , 1996, Medicina clinica.