Survival Analysis - Pros and Cons

Bottom-line:

• Kaplan-Meier is simple, but overly simple and doesn’t work well for estimation b/c it is non-parametric and you can’t easily estimate numbers that in-between times.
• Weibull is an exponential model which has a hazard that can increase proportionally as time (t) progresses, which is not always realistic
• Proportional Hazards is most accurate b/c the Hazard can fluctuate as Time goes on, but it’s also the most complicated and you can’t estimate the survival function.

Models

Kaplan Meier

• Pros
  • Simple
  • You can estimate the survival
• Cons
  • No functional form - no simple mathematical function that describes it
  • Can not estimate the hazard ratio
  • Can only include a few categorical x’s

Exponential

• Pros
  • Can estimate S(t) and HR
• Cons
  • Not always realistic
    • Weibull (parametric) allows HAZ to increase/decrease proportionally with time, but this isn’t realistic all the time either
    • Assumes a constant hazard, which is bad. E.g.
      • as humans our risk of dying increases as we get older
      • as babies we have a low risk, then higher risk as teens (risky behavior), then lower again at 30-40, then higher again as we go >60-70

Cox Proportional Hazard

• 113.020.020.50 Survival Analysis - Proportional Hazards PH
• Pros
  • Hazard can fluctuate with time, can increase/decrease as time goes by
  • Can estimate the hazard ratio
• Cons
  • Can not estimate the survival function S(t)