Cox ph model with icenReg: how to code data without event indicator

Question

I want to analyze my data with the interval-censored cox regression of the icenReg package. I have 5 time-points (1,2,3,4,5). Events can only happen once. Each person starts with baseline (T1). People were asked whether the event happend since the last interview. Thus there are 4 intervals (1-2, 2-3, 3-4, 4-5) in which the event can occurr.

My data looks like this:

ID1: the event happened between timepoint 2 and 3

ID2: no event happened throughout the study period (baseline T1 until T5)

ID3: the event happend between timepoint 1 and 2

ID4: the event happened between timepoint 3 and 4

ID5: no event happend, but the person dropped out of the study before end of its study period (i.e. T3 instead of T5)

In icenReg, data must provided in the following format:

fit_ph <- ic_sp(cbind(left, right) ~ covariate1, model = 'ph', bs_samples = numberofbootstrapsamples, data = data)

However, I'm unsure how to code my data correspondingly. In the case of no event, I would code the left side of the interval as T1 (baseline) and the right side as the time of drop-out or study completion. In the case of an event, I would code the left side of the interval as the assessment before the event and the right side of the interval as the assessment after the event.

This would look like this:

ID1: left 2, right 3

ID2: left 1, right 5

ID3: left 1, right 2

ID4: left 3, right 4

ID5: left 1, right 3

However, I'm unsure whether this is the correct approach. I am especially concerned regarding whether it is correct to represent 1) the right side of the interval in the case of no event with the corresponding time of drop-out or study completion (instead of Inf), because without an event indicator this somehow indicates an event in this period and 2) the left side of the interval in the case of an event as the assessment before the event (instead of the baseline assessment T1).

The topic was already similarly discussed in this (Why does icenReg or survival's "interval2" not accept event indicator?) post, but this question is somewhat beyond this discussion.

Answer 1

I would argue that the discussion you linked contains everything you need to answer this, but let's run through it.

The "interval2" syntax is used to indicate that an event occurred within the interval $(t_1, t_2)$ if both of these are finite. You can replace either end of the interval with (minus) Inf or NA to indicate censoring. Here, a non-finite $t_1$ indicates left censoring (you only know an upper bound on the time to event), and non-finite $t_2$ indicates right censoring (you only know the lower bound). It's not explicitly mentioned but I assume that both being non-finite is uninformative and discarded.

In your particular dataset there is only interval and right censoring. Specifically, ID1, ID2, and ID4 are observed events which you would like to interval-censor, and the values you propose are valid (conditional on the way you count time with baseline being $t=1$). However, ID2 and ID5 are right censored, so their $t_2$ value should be non-finite (Inf or NA). The only difference between these two is where the lower bound for the putative event time is; for ID2 this is $t_1=5$ and for ID5 this is whatever their last recorded timepoint is.