Abstract
Gronnesby and Borgan (1996) propose an overall goodness-of-fit test for the Cox proportional hazards model. The basis of their test is a grouping of subjects by their estimated risk score. We show that the Gronnesby and Borgan test is algebraically identical to one obtained from adding group indicator variables to the model and testing the hypothesis the coefficients of the group indicator variables are zero via the score test. Thus showing that the test can be calculated using existing software. We demonstrate that the table of observed and estimated expected number of events within each group of the risk score is a useful adjunct to the test to help identify potential problems in fit.
Similar content being viewed by others
References
P. K. Andersen, “Testing goodness of fit of Cox's regression and life model,” Biometricsvol. 38 pp. 67–77, 1982.
P. K. Andersen, Ø. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag: New York, 1993.
W. E. Barlow and R. L. Prentice, “Residuals for relative risk regression,” Biometrikavol. 75 pp. 65–74, 1988.
N. Breslow, “Discussion on 'Regression models and life tables' by D. R. Cox,” Journal of the Royal Statistical Society Series Bvol. 34 pp. 216–217, 1972.
C. H. Chen and P. C. Wang, “Diagnostic plots in Cox's regression model,” Biometricsvol. 47 pp. 841–850, 1991.
D. Collett, Modelling Survival Data in Medical Research, Chapman and Hall: London, 1994.
D. R. Cox, “Regression models and life-tables,” Journal of the Royal Statistical Society Series Bvol. 34 pp. 187–220, 1972.
A. J. Dobson, An Introduction to Generalized Linear Models, Chapman and Hall: London, 1990.
T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, Wiley: New York, 1991.
P. M. Grambsch and T. M. Therneau, “Proportional hazards tests and diagnostics based on weighted residuals,” Biometrikavol. 83 pp. 515–526, 1994.
P. M. Grambsch, T. M. Therneau and T. R. Fleming, “Diagnostic plots to reveal functional form for covariates in multiplicative intensity models,” Biometricsvol. 51 pp. 1469–1482, 1995.
R. Gray, “Some diagnostic methods for Cox regression models through hazard smoothing,” Biometricsvol. 46 pp. 93–102, 1990.
R. Gray, “Spline-based tests in survival analysis,” Biometricsvol. 50 pp. 640–652, 1994.
J. K. Grønnesby and Ø. Borgan, “A method for checking regression models in survival analysis based on the risk score,” Lifetime Data Analysisvol. 2 pp. 315–328, 1996.
T. Hastie and R. Tibshirani, “Exploring the nature of covariate effects in the proportional hazards model,” Biometricsvol. 46 pp. 1005–1016, 1990.
D. W. Hosmer and S. Lemeshow, “Goodness-of-fit tests for the multiple logistic regression model,” Communications in Statisticsvol. A10 pp. 1043–1069, 1980.
D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, Wiley: New York, 1989.
D. Y. Lin, L. J. Wei and Z. Ying, “Checking the Cox model with cumulative sums of martingale-based residuals,” Biometrikavol. 80 pp. 557–572, 1993.
N. H. D. Nagelkerke, J. Oosting and A. A. M. Hart, “A simple test for goodness of fit of Cox's proportional hazards model,” Biometricsvol. 40 pp. 483–486, 1984.
A. N. Pettitt and I. Bin Daud, “Investigating time dependence in Cox's proportional hazards model,” Applied Statisticsvol. 39 pp. 313–329, 1990.
C. Quantin, T. Moreau, B. Asselain, J. Baccario and J. Lellouch, “A regression survival model for testing the proportional hazards hypothesis,” Biometricsvol. 52 pp. 874–885, 1996.
D. Schoenfeld, “Chi-squared goodness-of-fit tests for the proportional hazards regression model,” Biometrikavol. 67 pp. 145–153, 1980.
M. Schumacher and M. Vaeth, “On a goodness-of-fit test for the proportional hazards model,” EDV in Medizin und Biologievol. 15 pp. 19–23, 1984.
T. M. Therneau, P. M. Grambsch and T. R. Fleming, “Martingale based residuals for survival models,” Biometrikavol. 77 pp. 147–160, 1990.
A. A. Tsiatis, “A note on a goodness-of-fit test for the logistic regression model,” Biometrikavol. 67 pp. 250–251, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
May, S., Hosmer, D.W. A Simplified Method of Calculating an Overall Goodness-of-Fit Test for the Cox Proportional Hazards Model. Lifetime Data Anal 4, 109–120 (1998). https://doi.org/10.1023/A:1009612305785
Issue Date:
DOI: https://doi.org/10.1023/A:1009612305785