How to calculate the differences of the least squares means in the inverse linked scale in poisson

[Jiangwei]

Hi, 

I am now using the PROC GENMOD to do the poisson regression to obtain the incidence rate of the outcome, I can get the incidence rate of the outcome in two exposure levels by using ILINK option in the LSMEANS.  Then I want to get the incidence rate difference between two exposure levels by using the DIFF option in the LSMEANS, however, it does not provide the difference's estimate and its confidence intervals on the scale of the mean (the inverse linked scale). Does anyone help me? And what is the inverse linked scale of poisson? I am really confused about the transformation from  -4.2980 into 0.01360. can anyone show me how to do the transformation? Thanks.

Below is the code and the SAS output.

proc genmod data=anadata. diet;
         class hieng_c;
         model chd = hieng_c / dist=poisson link=log offset=log_follow_time;
		 lsmeans hieng_c/diff=control means ilink cl plots=none;
         run;

[PaigeMiller]

e to the power -4.298 gives you the mean shown.

I don't know why the differences don't show up on the original scale.

[Jiangwei · Accepted solution]

Thank you for your reply!

After reading more materials, I find that difference in rates cannot be directly obtained from the LSMEANS, but can be obtained by using NLMeans macro, the NLEstimate macro, or from PROC NLMIXED, see this website for reference (http://support.sas.com/kb/37/344.html )