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?
