Cox Proportional Hazards Regression Models for Survival Data in Cancer Research

  • Mei-Jie Zhang
Part of the Cancer Treatment and Research book series (CTAR, volume 113)


Survival analysis which studies the distribution of life times is one of the most commonly used statistical techniques in cancer research. Most frequently, the Kaplan-Merir (1958) estimator is used to estimate the survival probability and log-rank test is used to compare the survival probabilities between the treatment groups. However, in cancer research, some prognostic factors, such as patient characteristics and treatment-related risk factors, may be associated with outcomes. Patients and biomedical researchers may want to know “which prognostic factors are associated with the outcome?”, “how does the prognostic factors affect the outcome?”, “does the risk factor have the same effect for different treatments?”, “what is the predicted survival probability at a certain time after the treatment for a particular patient?”, or “which treatment has better survival probabilities when adjusted for prognostic factors?”. We can use regression analysis to answer these questions. Cox (1972) proposed a proportional hazards regression model in analyzing the survival data. It has gained enormous popularity. We will discuss the techniques used in fitting a Cox regression model. Most of these techniques have been introduced and discussed in various books. Klein and Moeschberger (1997) gives an introduction and a number of examples to the Cox model. Fleming and Harrington (1991) and Andersen et al (1993) give a detailed theoretical discussions for these techniques.


White Blood Cell Count Conditioning Regimen Cell Dose Karnofsky Score Proportionality Assumption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersen, P. K. (1982). Testing goodness-of-fit of Cox’s regression and life model. Biometrics, 38: 67–77. 1982. Correction: 40: 1217.Google Scholar
  2. Andersen, P. K., Borgan, 0., Gill, R. and Keiding, N. (1993). Statistical Model Based on Counting Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
  3. Barrett, A. J., Ringdén, O., Zhang, M. J., Bashey, A., Cahn, J. Y., Cairo, M. S., Gale, R. P., Gratwohl, A., Locatelli, E, Martino, R., Schultz, K. R., Tiberghien, R., and GVHD/GVL Working Committee of the International Bone Marrow Transplant Registry. (2000). Effect of nucleated marrow cell dose on relapse and survival in identical twin bone marrow transplants for leukemia. Blood, 95: 3323–3327.Google Scholar
  4. Breslow, N. E. (1974). Covariance analysis of censored survival data. Biometrics, 30: 89–99.PubMedCrossRefGoogle Scholar
  5. Cleveland, W. S. (1979). Robust locally weighted regression and smoothing scatter plots. Journal of the American Statistical Association, 74: 829–836.CrossRefGoogle Scholar
  6. Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34: 187–220.Google Scholar
  7. Fleming, T. R. and Harrington, D. P. (1991). Counting Process and Survival Analysis. John Weley and Sons, New York.Google Scholar
  8. Kaplan, E. L. and Meier, P. (1958). Non-parametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457–481.CrossRefGoogle Scholar
  9. Klein, J. P. and Moeschberger, M. L. (1997). Survival Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York.Google Scholar
  10. Lin, D. Y., Wei, L. J. and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingales-based residuals. Biometrka, 80: 557–572.CrossRefGoogle Scholar
  11. Zhang, M. J. and Klein, J. P. (2001). Confidence bands for the difference of two survival curves under proportional hazards model. Lifetime Data Analysis, 7: 243–254.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Mei-Jie Zhang
    • 1
  1. 1.Medical College of WisconsinMilwaukeeUSA

Personalised recommendations