Survival analysis with recurrent events with subjects that move in and out of risk periods

Question

I would like to model a recurrent event with subjects that move in and out of risk over the course of the observation period of the study.

I have data on the out-of-risk periods (start and end dates) where the subject cannot experience the event. In my reading of this topic, I believe that this situation is referred to as "interval truncation" or "gaps", where subjects are "unobserved" for periods. And to best represent this, my data should be structured in counting process format, with start stop times that reflect these "gaps" in observations of each subject.

Q1. I would like to confirm that my understanding is correct and this would be an appropriate approach? If not, suggestions of better approaches are welcomed!

Q2. If interval truncation is the way to go, I would appreciate any help on how to convert my data to this counting process format with start stop times that reflect both event occurrence and unobserved periods in R. I can convert the data to counting process format with event occurrence, but do not know how to partition my start stop times to reflect unobserved periods (other than manually creating the data set which I would very much like to avoid).

Other useful info about my study:

• Subjects have a common start time of 0 months.
• Subjects are right-censored.
• Subjects are observed for 3 years.
• Subjects can move in and out of risk for varying amounts of time and frequency during the 3 year observation period.

Thank you!

Answer 1

Yes interval censoring is a way to handle this. The trick is to format it like any plain ol' right censored analysis. So one subject will result in two records when they have an interval censored period. The first record has time $0$ to time $t_1$ when they go off study and the event indicator set to $0$, then the second record has time $t_2$ to time $t_3$ where they experience the event (or don't as indicated by the censoring variable). The trick is time $t_2 > t_1$.

Handling multiple events can be done a few ways. The easiest is just the same as above. As soon as the event happens, say at time $t_1$, re-enter them in the study with a new record starting at time $t_1$ and following the patient until experience of their next event (if any).

People hem and haw about using methods for dependent data in these scenarios. A few applied examples and simulations have convinced me the interpretation of the above method is usually not far off from more complicated frailty models. For extra assurance, you can use a robust error estimator by specifying clusters within subject.

Sometimes a useful addition to these models is adding a covariate which either indicates whether the event has occurred or how many times it has occurred. For instance, in a cohort of subjects at risk for contracting a disease that is marked by "flare ups" has a much lower hazard until the patient in fact has the disease, at which point the flare ups occur much more frequently (so a diseased indicator is useful here).