I am running a Poisson model in sas comparing the number of ER visits after a surgery between 2 diseases in a given year. For those patients who were diagnosed later on in the year however, we have less follow up time to capture the ER visit so I decided to offset by the month of the surgery. I am wondering if someone may help in interpreting the estimates produced in the model with this offset term.
The time unit that you choose for your offset calculation will determine the units of your estimates. For example, a Poisson process with mean 10 per month, during a varying number of months :
data test; call streaminit(7); do id = 1 to 20; mth = rand("integer", 12); logmth = log(mth); logyr = log(mth/12); n = rand("Poisson", mth*10); output; end; run; title "Time expressed in months"; proc genmod data=test; model n = / dist=Poisson offset=logmth; run; title "Time expressed in years"; proc genmod data=test; model n = / dist=Poisson offset=logyr; run;
Notice how the exponentiated mean estimate is multiplied by 12 when offset is expressed in years instead of months..