# 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;

• "examine the effect of the treatment on the dependent variable while controlling for LOS"... If LOS is your dependent variable, you can't be controlling for it, for then it would appear on both sides of the equation. Is it your DV (in which case you're not controlling for it) or is it a covariate (in which case, it's not your dependent variable)? This confusion in your question cannot lead to good answers. – Glen_b Jan 2 '15 at 3:13
• Thanks, Glen_b for pointing that out. You are exactly right. I've edited my question accordingly. The LOS is my DV -- I'm not controlling for it. I guess that's what happens when you make a most at 3:30 in the morning. ;-) – StatsStudent Jan 12 '15 at 8:34
• Just a note on the "offset" - this would be appropriate for a rate type variable. You offset to account for higher/lower "exposure" to an event happening. For example, modelling number of times the nurse was called - you would include an offset. The LOS doesn't need one. One way to see this is try to answer - model LOS per what? Difficult to fill in the "what". – probabilityislogic Jan 12 '15 at 8:44