I wish to model the number of days patients stayed in a clinic. Some of my predictors included: type of injury/disease, age, insurance, etc. Since days are count data and my data is over-dispersed, negative binomial models seem to be the appropriate technique. However, I know that when using count models the exposure time should be fixed (ex. days absent in a school during a year) or at least control for the exposure time (in Stata you can control this by adding the exposure option). Below are my questions.

1. Is it valid to model days using negative binomial models?

2. How can I control for the exposure time? Is this necessary?

3. Can you recommend good reads that cover this topic, using number of days as the dependent variable?

4. Any other ideas?

Thank you in advance,

Marvin