Advertisement

Survival Analysis

Protocol
Part of the Methods in Molecular Biology™ book series (MIMB, volume 404)

Abstract

This chapter introduces some fundamental results in survival analysis. We first describe what is censored failure time data and how to interpret the failure time distribution. Two nonparametric methods for estimating the survival curve, the life table estimator and the Kaplan-Meier estimator, are demonstrated. We then discuss the two-sample problem and the usage of the log-rank test for comparing survival distributions between groups. Lastly, we discuss in some detail the proportional hazards model, which is a semiparametric regression model specifically developed for censored data. All methods are illustrated with artificial or real data sets.

Key Words

Actuarial estimator Cox model nonparametric methods product-limit estimator rank testing right censoring semiparametric regression 

References

  1. 1.
    Cox, D. R., and Oakes, D. (1984) Analysis of Survival Data. London, Chapman & Hall, pp. 52–53.Google Scholar
  2. 2.
    Ware, J. H., and DeMets, D. L. (1976) Reanalysis of some baboon descent data. Biometrics. 32, 459–463.PubMedCrossRefGoogle Scholar
  3. 3.
    Kalbfleisch, J. D., and Prentice, R. L. (2002) The Statistical Analysis of Failure Time Data. New York, Chichester, John Wiley & Sons.Google Scholar
  4. 4.
    Klein, J. P., and Moeschberger, M. L. (1997) Survival Analysis Techniques for Censored and Truncated Data. New York, Springer-Verlag, pp. 100–103.Google Scholar
  5. 5.
    Kaplan, E. L., and Meier, P. (1958) Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc. 53, 457–481.CrossRefGoogle Scholar
  6. 6.
    Efron, B. (1967) The two sample problem with censored data. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. New York, Prentice-Hall, 4, pp. 831–853.Google Scholar
  7. 7.
    Gill, R. D. (1980) Censoring and Stochastic Integrals, Mathematical Center Tracts 124. Amsterdam, Mathematisch Centrum.Google Scholar
  8. 8.
    Klein, J. P. (1991) Small-sample moments of some estimators of the variance of the Kaplan-Meier and Nelson-Aalen estimators, Scand. J. Stat. 18, 333–340.Google Scholar
  9. 9.
    Greenwood, M. (1926) The errors of sampling of the survivorship tables. In: Reports on Public Health and Statistical Subjects, no. 33. London, HMSO, Appendix 1.Google Scholar
  10. 10.
    Gehan, E. A. (1965) A generalized Wilcoxon test for comparing arbitrarily singlycensored samples. Biometrika 52, 203–223.PubMedGoogle Scholar
  11. 11.
    Harrington, D. P., and Fleming, T. R. (1982) A class of rank test procedures for censored survival data. Biometrika 69, 553–566.CrossRefGoogle Scholar
  12. 12.
    Cox, D. R. (1972) Regression models and life-tables (with discussion). J. R. Stat. Soc. Ser. B Methodol. 34, 187–220.Google Scholar
  13. 13.
    Cox, D. R. (1975) Partial likelihood. Biometrika 62, 269–276.CrossRefGoogle Scholar
  14. 14.
    Breslow, N. E. (1975) Analysis of survival data under the proportional hazards model. Int. Stat. Rev. 43, 45–58.CrossRefGoogle Scholar
  15. 15.
    Cox, D. R., and Snell, E. J. (1968) A general definition of residuals (with discussion). J. R. Stat. Soc. Ser. B Methodol. 30, 248–275.Google Scholar
  16. 16.
    Schoenfeld, D. (1982) Partial residuals for the proportional hazards regression model. Biometrika 69, 239–241.CrossRefGoogle Scholar
  17. 17.
    Lin, D. Y. Wei, L. J., and Ying, Z. (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika. 80, 557–572.CrossRefGoogle Scholar
  18. 18.
    Therneau, T. M., and Grambsch, P. M. (2000) Modeling survival data: extending the Cox model. Berlin, New York, Springer-Verlag.Google Scholar
  19. 19.
    Freireich, E. J., Gehan, E., Frei, E., Schroeder, L. R., Wolman, I. J., Anbari, R., Burgert, E. O., Mills, S. D., Pinkel, D., Selawry, O. S., and others. (1963) The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potentially useful therapy. Blood 21, 699–716.Google Scholar

Copyright information

© Humana Press Inc., Totowa, NJ 2007

Authors and Affiliations

  1. 1.Department of BiostatisticsHarvard School of Public HealthBoston
  2. 2.Department of Statistics and BiostatisticsUniversity of Wisconsin—MadisonMadison

Personalised recommendations