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113 Math

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113.020.010.10.30 Regression models - Diff between Expo vs Weibull vs Cox

# Difference between Expo vs Weibull vs Cox

These notes reference the equations from 113.020.010.10.20 Regression models - Exponential Distribution, especially the last two with b-naught.

### Exponential

- b-naught is a constant - it is a number
- It doesn't change, there is no time in the function, so it doesn't change over time
- Constant hazard
- This is the same as PH, but not named after it

- Constant hazard

### Weibull

- b-naught increases/decreases
*proportionally*with time - b-naught is
`ln(\alpha) * ln(t) + b-naught`

- So you can see that as time gets bigger, the b-naught gets proportionally bigger

### Cox

- b-naught can fluctuate, it can increase/decrease with time, multiple times
- b-naught is
`ln(h-naught(t))`

- Can estimate all the coefficients in the model w/o having to specify the function
- This function is good for effect-size models, doesn't work for predictive models where you want to predict/estimate survival

##### Source:

- Me