I am looking for most suitable model for count data in the following case:
- we collect number of patient's visits in a hospital for $t_i$ days ($t_i$ varies across subjects)
- some patients died during the study time ($t_i$ is the number of days since we started observing them till their death), some did not ($t_i$ is the number of days since we started observing them till their last update)
- number of patient's visits in a hospital may be equal to 0 (this is not 0-truncated case)
- there is no explicit information that patient is / is not undergoing i.e. some particular disease which could make him visit hospital at least once or is in a condition that would make him not visit at all
This is not a randomized clinical trial. I have demographical variables in my dataset (age, race, gender) as well as some health-related variables (MBI, has kidney disease, has hypertension, others).
My goal is to examine factors associated with increased hospital visits.
What count data model should be used to model number of visits in a hospital?