What if events also have factors, not only the studied subjects!!

Hello everyone...

despite my a little knowledge in survival analysis and its available models.... I have the following question:
What I know that Cox models offer a hazard function, with the assumption of proportionality of the hazard for different studied subjects.
The frailty component can used as a multiplicative random effect to model unobserved
subject-specific factors.

Now the question is, is there any model which incorporate event specific factors, such as a degree of illness or the damage of a disaster? and how does the likelihood function look like?



Ninja say what!?!
hmmm. I'm not sure I have this understood well, but let me give it a shot.

Instead of analyzing a dichotomous outcome (such as and event happening), you want to analyze the degree of the outcome. So for example, you want to look at the degree of illness only among people who are already sick. Is this right?

If so, the model choice really depends on the distribution and assumptions you want to make. I'd like to see the distribution of the outcome before offering suggestions.