Estimating the Survival and Hazard Functions

  • Terry M. Therneau
  • Patricia M. Grambsch
Part of the Statistics for Biology and Health book series (SBH)


This chapter gives an introduction to the simplest concept: estimating the survival curve when there are no covariates. Although simple, it forms a platform for understanding the more complex material that follows. We do it twice, once informally (although making use of counting process ideas) in Section 1, and then a second time with the connections to counting processes and martingales much more complete. Sections 2 and 3 first give an overview of the necessary theory and then apply it to the informal results of Section 1, both validating and extending them. Section 4 discusses the extension to tied data. The reader might want to focus on Section 1 on the first reading, perhaps supplemented with the results (but not derivations) of Sections 3 and 4.


Hazard Function Failure Time Counting Process Cumulative Hazard Asymptotic Relative Efficiency 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Terry M. Therneau
    • 1
  • Patricia M. Grambsch
    • 2
  1. 1.Department of Health Sciences ResearchMayo ClinicRochesterUSA
  2. 2.Division of Biostatistics, School of Public HealthUniversity of MinnesotaMinneapolisUSA

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