Is there a way to perform two regressions sequentially: one for a binary outcome and one for a "time to event" one?

[Federico Tedeschi]

Dear Statalisters,

I'm using Stata 17.0.

I'd like to perform two regressions simultaneously: the first one for a binary outcome (event vs no-event); in case of no-event, then observations will be included in the second regression, that is a "time to event" one. I happened to use commands like "seqlogit" (but here the problem is that the second regression can't be a logit one) and "cmp" (that doesn't include models for "survival analysis"): I would need something like that.

Actually, to describe my situation more in detail, I have a similar situation as here:
https://stats.stackexchange.com/q/604396/159259

In my case, however, the problem is not left-censoring: my data are not censored; in fact I know when "the event before the event" is. Indeed, in my case this corresponds to relapse or withdrawal symptoms while the therapy is tapering down (so, before it stops). The problem is that I can't take that time (after the beginning of the therapy) as it is, since I have patients in the two groups following a different tapering-down strategy: the time to the drug going to zero differs between the two groups (4 weeks for one group, 16 weeks for the other one). Thus, the binary outcome in my case is: reaching the end of the therapy without withdrawal nor relapse, while the time-to-event one is: withdrawal or relapse after the end of the therapy.

Thus, since the end of the therapy would be time 0 in my case, another way to see it is: a time-to-event model with a mass point at 0, but this seems to me a statistical blasphemy, as long as time-to-event models only allow positive survival times.

[Federico Tedeschi]

I could have found a solution, but I’m not sure.
The example here: https://www.stata.com/manuals/fmmexample4.pdf
describes this situation: a cure model, where a fraction of the population never experiences a failure. Here, I see some differences:
A1) my case is somehow reversed: a fraction of the population already experiences failure even before time 0;
A2) I exactly know who belongs to Class 1 (failure before the event) and who to Class 2 (those participating to survival analysis), while in the example you know that some people for sure are non-cured (the ones experiencing the events), but for the others you are uncertain. Thus, you know that some people for sure belong to Class 1, but for the others you are unsure.

However, there is also a similarity:

B) If you belong to Class 2, you undergo survival analysis; if you belong to Class 1, you don't.

To sum up: in the example, “pointmass fail” means: “when you belong to Class 1, then fail = 0”. In my case, can I use “pointmass fail” to mean: “when you belong to Class 1, then you fail before survival analysis starts”? And, does the fact that my classes are entirely known prevent me from using the "fmm" command?