I am analyzing a dataset with recurrent events, and considering two candidate models:
- A model based on a renewal process (time is measured from the previous event)
- A model based on an inhomogeneous Poisson process (all events share the same time reference)
I would like to make a principled decision about which type of model is more suitable, and looking for ideas.
- A similar (but more specific) question was asked here
- In reality, both my models are modified to account for the number of previous events, but I believe that this is not crucial at this point
I was asked to provide additional information about the dataset and the problem. However, I would not want to load the question with inessential details, so I keep it generic:
Dataset: thousands of specimen with dates of events and specimen-specific covariates for each. For some no events has occured (i.e. they are right-censored)
Problem: we are dealing with equipment failures here. After a failure the equipment is repaired and put back in service. However, the risk of failure likely increases, if previous failures took place. Thus, the difference between the two types of models is
a) whether we attribute failures to the fact that this particular piece of equipment is failure prone (fraility?) or b) whether failure is more likely for older equipment.