I am working with data that follows Epilepsy patients from first seizure until up to two years of follow up. I'm comparing the number of MRIs they've received during their follow up between two time periods: before we established a clinic "Before Group" and after we established a clinic "After Group".
I'm using a negative binomial model with counts as dependent variable, log(follow up time) as offset, group as independent variable, and some other covariates I'm adjusting for.
We expect that the bulk of the MRIs will occur early in the follow up times. We have shorter follow up times for our patients who were treated in the Before Group. Many only have 3-6 months. If we calculate mean number of MRIs/year for the two groups, would the "annualizing" of the counts for the two groups make it seem like the Before Group had more than they actually had, because there isn't a uniform probability of them having a MRI over the year (because the bulk of MRIs happen at the beginning)?