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113 Math

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113.020.020.30 Survival analysis - Pros and cons

# 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

- Can estimate
- 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

- Not always realistic

## 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)`

- Can not estimate the survival function

##### Source:

- Me