For a poisson regression for SMR, how to incoporate both personyear and expected death in "offset"

[cocoono]

In this case, I have information on person year and standard mortality rate for each stratum. As I checked the materials online, no one used two offsets at the same time. So I'm wondering can I do this? (the following is the SAS code)

proc genmod data=bomb3;
model casenum = age followuptime dose
/ dist=poisson offset=logcancerexp offset=logpys;
run;

[StatDave · Accepted solution]

An offset is used when you want to model a rate rather than just a count. See this note that discusses this. Since there is only a single count response, there can only be one offset that serves as the denominator of the rate. I assume that CASENUM is your count of the event of interest. If you want to model the rate per person-year, then you just need to specify the log of the person-year variable in OFFSET=. If you want to involve SMR in the model, simply include it as another predictor in the model. Note that an offset variable (as explained in the note above) is just a model predictor with its parameter restricted to one which is how it becomes the rate denominator. 

[cocoono]

Thank you for your reply! I listed down the equation, and I think maybe the log(person-year) is no longer required using SMR. It's seems that I only need to consider log(expected) as the offset. How do you think?