Advertisement

Nonparametric and Semiparametric Models

  • David D. HanagalEmail author
Chapter
Part of the Industrial and Applied Mathematics book series (INAMA)

Abstract

Survival data are conveniently summarized through estimates of the survival function and hazard function. Methods of estimating these functions from a sample of survival data are said to be nonparametric or distribution-free since they do not require specific assumptions to be made about the underlying distribution of the survival times. An initial step in the analysis of survival data is to present numerical or graphical summaries of the survival times for individuals in a particular group. Such summaries may be of interest in their own right, or as a precursor to a more detailed analysis of the data. Once the estimated survival function has been found, the median and other percentiles of the distribution of survival times can be estimated. When the survival times of two groups of patients are being compared, an informal comparison of the survival experience of each group of individuals can be made using the estimated survival functions. However, there are more formal procedures that enable two groups of survival data to be compared. Nonparametric procedure for comparing two or more groups of survival times is the logrank test which is the most powerful test against the alternatives that the hazard functions are proportional.

References

  1. Breslow, N.E.: Discussion of professor Cox’s paper. J. R. Stat. Soc. B 34, 216–217 (1972)MathSciNetGoogle Scholar
  2. Breslow, N.E.: Covariate analysis of censored survival data. Biometrics 30, 89–100 (1974)CrossRefGoogle Scholar
  3. Cox, D.R.: Regression models and life tables (with discussions). J. R. Stat. Soc. B 34, 187–220 (1972)Google Scholar
  4. Cox, D.R.: Partial likelihood. Biometrika 62, 269–276 (1975)MathSciNetCrossRefGoogle Scholar
  5. Fleming, T.R., Harrington, D.P.: Nonparametric estimation of survival distribution in censored data. Commun. Stat. Theory Methods 13, 2469–2486 (1984)MathSciNetCrossRefGoogle Scholar
  6. Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc. 53, 457–481 (1958)MathSciNetCrossRefGoogle Scholar
  7. Nelson, W.: Hazard plotting for incomplete failure data. J. Qual. Technol. 1, 27–52 (1969)CrossRefGoogle Scholar
  8. Peto, R.: Contribution to the discussion of paper by D.R. Cox. J. R. Stat. Soc. B 34, 205–207 (1972)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Symbiosis Statistical InstituteSymbiosis International UniversityPuneIndia

Personalised recommendations