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

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