Survival Model with "treatments" at some point in time

Dear all,

I was glad to see that Stata 14 offers panel survival models, I am however unsure whether this is exactly what I need. I know this is not Stata-specific, but if you could advise me on the framework to look for, I'd be very happy. I want to model the following thing:

I observe people over a certain time period, one observation per month. I want to find the determinants of how long I observe them before they are "dead" (not really dead). In particular, I want to examine the effect of some event e happening to them on the probability of their death. This event e happens on different dates for different people and does not happen to all. But if it happens, then only once. this means: once dead, always dead.

In ordinary survival models with one observation per person I cannot properly model the time dynamics, correct? So that's why I thought panel survival models are interesting, but then Statacorp says that this is really only for multiple deaths per person.

I might need to add that my other covariates (not only treatment e 0/1) change over time, but also the others, so I really feel like I need to introduce the time structure on the analysis.

Can anyone give me some guidance on this issue?
Thank you,

Doro