proc countreg: how to account for population/denominator

[Cruise]

Hi folks:

@ballardw @Reeza 

Do you know how I could adjust the covariates in PROC COUNTREG  to the population size? In poisson regression model, for example, I define the denominator population using link and offset functions as shown in proc genmod below. According to SAS doc on proc countreg, offset seems to be intended for zero inflated models which is not the case for my data. I'd love to discuss with somebody who has an experience of using proc countreg about the proper use of offset and link functions. 

proc genmod data=have;
class vars/param=ref;
model OUTCOME=covariates/dist=negbin link=log offset=ln;
run;

my proc countreg looks like below using one covariate with spatial effect as an example. But I have to account the covariate to the population size now. 

proc countreg data=combined2 Wmat=Wmatrix;
   model n_outcomes = kindergarten_count / dist=negbin offset=ln;
   spatialeffects kindergarten_count;
run;  

model runs where ln=log(pop). but i'm not sure if this was the right decision.