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Estimating the Survival and Hazard Functions

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

Abstract

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.

Keywords

Hazard Function Failure Time Counting Process Cumulative Hazard Asymptotic Relative Efficiency 
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.

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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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