Survival Analysis

  • Lawrence M. Friedman
  • Curt D. Furberg
  • David L. DeMets


This chapter reviews some of the fundamental concepts and basic methods in survival analysis. Frequently, event rates such as mortality or occurrence of nonfatal myocardial infarction are selected as primary response variables. The analysis of such event rates in two groups could employ the chi-square statistic or the equivalent normal statistic for the comparison of two proportions. However, when the length of observation is different for each participant, estimating an event rate is more complicated. Furthermore, simple comparison of event rates between two groups is not necessarily the most informative type of analysis. For example, the 5-year survival for two groups may be nearly identical, but the survival rates may be quite different at various times during the 5 years. This is illustrated by the survival curves in Fig. 15.1. This figure shows survival probability on the vertical axis and time on the horizontal axis. For Group A, the survival rate (or 1 − the mortality rate) declines steadily over the 5 years of observation. For Group B, however, the decline in the survival rate is rapid during the first year and then levels off. Obviously, the survival experience of the two groups is not the same although the mortality rate at 5 years is nearly the same. If only the 5-year survival rate is considered, Group A and Group B appear equivalent. Curves like these might reasonably be expected in a trial of surgical versus medical intervention, where surgery might carry a high initial operative mortality.


Survival Curve Hazard Rate Survival Experience Stagger Entry Estimate Survival Curve 
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Copyright information

© Springer New York 2010

Authors and Affiliations

  • Lawrence M. Friedman
    • 1
  • Curt D. Furberg
    • 2
  • David L. DeMets
    • 3
  1. 1.BethesdaUSA
  2. 2.School of MedicineWake Forest UniversityWinston-SalemUSA
  3. 3.Department of Biostatistics & Medical InformaticsUniversity of WisconsinMadisonUSA

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