Survival Analysis

  • Bryan Kestenbaum

Learning Objectives

  1. 1.

    Incidence measures do not fully describe the development of events over time.

  2. 2.

    The survival function, S(t) represents the probability of being alive at a particular time, t.

  3. 3.
    For a graphical presentation of the survival function:
    1. a.

      Survival for any particular follow-up time is estimated by a vertical line to S(t).

    2. b.

      Median survival is estimated by a horizontal line from S(t) = 0.5.

  4. 4.

    The logrank test evaluates whether whole survival curves are statistically different from each other.

  5. 5.

    Survival analysis is typically used to describe the first occurrence of a particular outcome.

  6. 6.

    Censoring occurs when a subject leaves a study before incurring the outcome of interest.

  7. 7.

    The Kaplan–Meier method is used to estimate S(t) in the presence of censoring.

  8. 8.

    Kaplan–Meier plots are typically unadjusted.

  9. 9.

    The Cox model can adjust for confounding and account for censoring.

  10. 10.

    The Cox model yields a hazard ratio, which very closely parallels the relative risk.

  11. 11.

    Hazard ratios are meaningful for studies in which the relative risk remains constant throughout the study period; studies with changing risks over time should present separate hazard ratios for the relevant time periods of interest.



Abdominal Aortic Aneurysm Survivor Function Abdominal Aortic Aneurysm Surgical Group Risk Time 
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  1. 44.
    United Kingdom Small Aneurysm Trial Participants. Long-term outcomes of immediate repair compared with surveillance of small abdominal aortic aneurysms. N Engl J Med. May 9 2002;346(19):1445–1452.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of WashingtonSeattleUSA

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