offset interpretation for proc genmode

[raheleh22]

I have count outcome data across multiple counties ( therefore, different population/ per county). I am considering Poisson Regression with count cases and using term offset being log population. here is my code: 

data ZZZZ;
SET ZZ;
ln = log(POPULATION);
RUN;
proc genmod data=ZZZZ;
class COUNTY (ref='1')/PARAM=REF;
WHERE TIME=1 ;
model case = X1 X2 / dist=poisson link=log offset=ln;
run;

I just wanted to make sure my code is considering population adjustment 

and how would be the interpretation. I got Estimates, are this estimates rates or it would be interpreted as : one unit increase in X, increase/decrease log cases? 

Thanks, 

[StatDave · Accepted solution]

The offset, log of population in your case, is just another predictor in the model. The only difference is that it is restricted to have a parameter estimate equal to 1. In the estimation process, all parameter estimates are adjusted for the presence of the others. Since the response function that you are modeling is the log of the Poisson mean, that is what the parameter estimates apply to. So, the X1 parameter is the effect of a unit increase in X1 on the log Poisson mean - the log mean count. However, computing a linear combination of the parameters, without involving the offset value, predicts the rate, not the mean. See the discussion of all this in this note. 

BTW, you should never specify a variable in the CLASS statement that is not used elsewhere in the model specification. Missing values in such variables will cause observations to be ignored which don't need to be. Since you are not using COUNTY in the model and it is the only thing in the CLASS statement, you should drop the CLASS statement.

[raheleh22]

This is really helpful. I am using COUNTY VARIABLE in my model and that is why I used CLASS statement for COUNTY. infact my X2 is COUNTY.
Thanks a lot