Advertisement

Lifetime Data Analysis

, Volume 4, Issue 2, pp 109–120 | Cite as

A Simplified Method of Calculating an Overall Goodness-of-Fit Test for the Cox Proportional Hazards Model

  • Susanne May
  • David W. Hosmer
Article

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.

Goodness-of-fit score test martingale residuals risk score 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. K. Andersen, “Testing goodness of fit of Cox's regression and life model,” Biometricsvol. 38 pp. 67–77, 1982.Google Scholar
  2. P. K. Andersen, Ø. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag: New York, 1993.Google Scholar
  3. W. E. Barlow and R. L. Prentice, “Residuals for relative risk regression,” Biometrikavol. 75 pp. 65–74, 1988.Google Scholar
  4. 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.Google Scholar
  5. C. H. Chen and P. C. Wang, “Diagnostic plots in Cox's regression model,” Biometricsvol. 47 pp. 841–850, 1991.Google Scholar
  6. D. Collett, Modelling Survival Data in Medical Research, Chapman and Hall: London, 1994.Google Scholar
  7. D. R. Cox, “Regression models and life-tables,” Journal of the Royal Statistical Society Series Bvol. 34 pp. 187–220, 1972.Google Scholar
  8. A. J. Dobson, An Introduction to Generalized Linear Models, Chapman and Hall: London, 1990.Google Scholar
  9. T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, Wiley: New York, 1991.Google Scholar
  10. P. M. Grambsch and T. M. Therneau, “Proportional hazards tests and diagnostics based on weighted residuals,” Biometrikavol. 83 pp. 515–526, 1994.Google Scholar
  11. 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.Google Scholar
  12. R. Gray, “Some diagnostic methods for Cox regression models through hazard smoothing,” Biometricsvol. 46 pp. 93–102, 1990.Google Scholar
  13. R. Gray, “Spline-based tests in survival analysis,” Biometricsvol. 50 pp. 640–652, 1994.Google Scholar
  14. 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.Google Scholar
  15. T. Hastie and R. Tibshirani, “Exploring the nature of covariate effects in the proportional hazards model,” Biometricsvol. 46 pp. 1005–1016, 1990.Google Scholar
  16. D. W. Hosmer and S. Lemeshow, “Goodness-of-fit tests for the multiple logistic regression model,” Communications in Statisticsvol. A10 pp. 1043–1069, 1980.Google Scholar
  17. D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, Wiley: New York, 1989.Google Scholar
  18. 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.Google Scholar
  19. 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.Google Scholar
  20. A. N. Pettitt and I. Bin Daud, “Investigating time dependence in Cox's proportional hazards model,” Applied Statisticsvol. 39 pp. 313–329, 1990.Google Scholar
  21. 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.Google Scholar
  22. D. Schoenfeld, “Chi-squared goodness-of-fit tests for the proportional hazards regression model,” Biometrikavol. 67 pp. 145–153, 1980.Google Scholar
  23. 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.Google Scholar
  24. T. M. Therneau, P. M. Grambsch and T. R. Fleming, “Martingale based residuals for survival models,” Biometrikavol. 77 pp. 147–160, 1990.Google Scholar
  25. A. A. Tsiatis, “A note on a goodness-of-fit test for the logistic regression model,” Biometrikavol. 67 pp. 250–251, 1980.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Susanne May
    • 1
  • David W. Hosmer
    • 1
  1. 1.Department of Biostatistics and EpidemiologyUniversity of Massachusetts at AmherstUSA

Personalised recommendations