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this is my first time asking a question so please be gentle.

I have never taken a course in survival analysis, but at work I am being tasked with fitting a survival model anyway. So I dove into a textbook from our library and started reading about it. I found that, after messing with hazard functions and the like, survival regression really just boils down to the following:

If $T$ is the response variable (time to failure), let $Y = \log T$. Covariates $Z$. If we fit the commonly used exponential or Weibull regression models, the model takes the form:

$$Y = \alpha + Z^T \beta + W$$

Where $W$ has an extreme value distribution (in the case of Weibull, scaled by a factor $\sigma$). From grad school, I am pretty well trained in GLMs. This looks a lot like a GLM, where the response is extreme value (Gumbel?) distributed. I haven't gotten into the specifics of how the models are actually computed, but I assume it will be some sort of IRLS.

Am I correct here? Or is there something inherently different about survival regression that makes it not a GLM?

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  • $\begingroup$ It requires data on time to event with possible right censoring for cases where the event has not occurred at the time of analysis. $\endgroup$ May 12, 2017 at 14:32
  • $\begingroup$ Yes, I know this, but does that in some way preclude it from being considered a GLM? If so, why? $\endgroup$ May 12, 2017 at 14:38
  • $\begingroup$ Maybe this one can give you some help on understanding the survival analysis: bit.ly/2ohX85g $\endgroup$
    – user158565
    May 12, 2017 at 15:17
  • $\begingroup$ See stats.stackexchange.com/questions/585057/… $\endgroup$ Sep 15, 2022 at 19:58

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