Negative Binomial Regression? I have a dependent count variable that measures the number of days spent in a hospital (LOS) for a group of patients who received two different medical interventions upon hospitalization.  I'm trying to examine the effect of the treatment on the dependent variable, LOS while controlling for other variables.  Would it be appropriate to use a negative binomial model here?  Normally, I'd think yes, but I'm a bit confused since everything I've read on Poisson and Negative Binomial regression says that I need to be using counts that have the same time period (or use an offset).  But in my case, the time, or days spent in the hospital, is my dependent variable.  Given this, would it still be appropriate to use negative binomial regression?  If it helps in providing an answer, I'm using the following SAS code (but am not sure if it's appropriate):
proc genmod data=work.hosp;
class trt gender;
model los = trt admissiondept age severity_index gender injscore / dist=negbin link=log type3;
run;

 A: Assuming LOS is intended as a DV and not a covariate, "Length of stay" is not really a count (in the required sense), but a (possibly discretized) duration. You wouldn't normally use a count model for that.
I'd be inclined toward using a survival model; that will also enable you to cope with the likely censoring (for people who are still in hospital when you stop taking data, for example -- you can't just leave them out because their duration wasn't finished, otherwise you'll be biasing against people with long LOS).
A: The advice you refers (that the count need to refer to the same length time intervals) seems to be irrelevant here.  That is meant for a situation where you are counting  number of point events within some time interval.  But your response variable is a duration, so a completely different situation.  So I think you could try with a Poisson (or negative binomial) regression, and then validate it with residual plots and so on. 
A: Negative binomial would still be appropriate. Poisson would be as well, if your data meets the equidispersion assumption. (If it does not, stick with nbreg.)
