Time to event without particularly modelling event rate

Hi everyone,

I got the time until an aftercare and want to assess the treatment effect on this time. However, I’m not particularly interested in whether the event occurs more often or not (i.e., not interested in the event rate like in cox regression). Thus, given the event occurs, I’m interested in the time until the event and want to compare these between the treatment groups.

My time variable is discrete (timepoint 2, 3, 4, 5) and interval-censored (i.e. I only know that the event happend between time point 1 and 2, 2 and 3 and so on). My treatment group is dichotomous (control vs. treatment group).

My question would be:

  1. How would you do hypothesis testing with this kind of data?
  2. Additionally out of curiosity, is there any technique on how to account for non-events? E.g., I could think about a sensitivity analysis in which you give non-events the theoretically assumed time until uptake of aftercare, if this is known. Imagine that it is known that uptake takes about 9 months, so non-events could be coded like this (e.g., timepoint 6)?

Keeping in mind that such an analysis is of the “look into the future” type and will not result in prospectively usable results, you can do a simple conditional analysis by subsetting on patients having an aftercare event and using ordinary or semiparametric regression to model the time until that event.

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