Recurrent event analysis: What approach to choose? I am trying to examine if the interval between recurrent suicide episodes becomes shorter over the course of repeated incidents. My data is in long format with each participant occupying multiple rows based on the number of attempts they made. Then for time-variable, I have time between 1st and 2nd attempt, the time between 2nd and 3rd attempt...all the way up to 6th attempt. If my question is to examine if the time between attempts decreases over attempts then what statistical approach is best suited to answer this question? I am leaning towards the hierarchical linear model (HLM) using time intervals between attempts as DV and the number of attempts as my predictor variable. However, someone suggested that the Frailty model (survival analysis) could be used as well. I have read about it but can't seem to understand how that might apply to my question. I want to understand if the Frailty model will be a better approach than HLM to answer my question.

In a survival model of recurrent events, a frailty model is similar to a random-effect model, although the assumed distribution of random effects isn't always the Gaussian distribution assumed in typical random-effect models. Therneau and Grambsch say on page 169:

multiple outcomes are assumed to be independent conditional on the per-subject coefficient.

That allows individuals to differ depending on some inherent "frailty" that puts each at different overall risk of the event.
At first, that independence assumption might not seem consistent with your goal:

I am trying to examine if the interval between recurrent suicide episodes becomes shorter over the course of repeated incidents.

However, if you incorporate the number of previous episodes as a predictor in the model, then the independence assumption is conditional both on the subject and that predictor, so you could be OK.
The reason you need to do something beyond a simple mixed model is that you must deal with "the interval between recurrent suicide episodes" when an individual survived a previous episode but hasn't had another yet at the last follow-up time. Those time intervals are necessarily right censored, as you only have a lower limit on how long that interval might end up being. That's where survival analysis helps, as it directly deals with that situation.
A way to combine these approaches would be "using time intervals between attempts as DV and the number of attempts as my predictor variable" in a frailty/random-effect survival model. You would, however, then include those last right-censored time intervals, coded appropriately, in the data presented to the model.
This page has an outline of ways to approach recurrent-event modeling, with a link to a textbook.
