Forcing coefficients for Generalized Linear Models and count models in proc genmod

[RobertWF1]

I'm working on a regression model where Y is inpatient counts distributed according to the zero-inflated negative binomial pdf. 

We'd like to fix the trend coefficient on the Y count in the prior 12 month period so that mean(Y_post) = 0.70*mean(Y_pre).

Having discovered the offset trick for forcing coefficients in proc genmod here, how would I construct the offset knowing it's a GLM and not a linear regression?

Do I first need to take a natural log transform of the trend constant since E(Y_post)=exp(beta0 + trend*Y_pre + beta1*x1 + beta2*x2 + ...) for the ZINB distribution?

Or does SAS handle the log transforms for me and I simply code as follows? 

%let trend = 0.70;
data analysis_data; 
set analysis_data; 
y_pre_trend = &trend*y_pre;
run;

proc genmod data=analysis_data; 
model y_post = x1 x2 x3 / offset=y_pre_trend dist=zinb;
zeromodel;
run;

[RobertWF1]

Found SAS Usage Note 22800: Restricting model parameters that seems to support the above interpretation:

https://support.sas.com/kb/22/800.html

[Ksharp]

I remember @Rick_SAS  wrote a blog about it before .

https://blogs.sas.com/content/iml/2020/09/16/restricted-regression-sas.html

[RobertWF1]

Thanks - this is an interesting read, but unfortunately only applies to linear regression models.