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I'm comparing two groups on the # of hospitalizations they have in a 5 year period. Length of hospitalization stay is highly variable. For example, a patient might have 3 hospitalizations that in total lasted 100 days, where as another patient might have had 50 visits, each lasting a single day. Therefore, It would seem natural to factor in length of stay (in days) into the picture.
Right now I'm thinking of a Poisson Rate Regression, with a single categorical predictor (Group) and # of hospitalizations as the DV. I'd like to include Total Length of hospitalization stays as an offset, which is in days. My question is, I have some patients who did not have any hospitalizations, therefore their length of stay is effectively 0.
In order to hit the Poisson Rate Regression model (in SAS anyway), I must log the offset term. I clearly can't take the log of 0, so I'm wondering what can I do in this situation? Can we add a constant of 1 to both Hospitalization and Total Length of Hospitalization to remedy this?
(cross posted @ Talkstats.com)