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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)

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marked as duplicate by kjetil b halvorsen, mdewey, Ferdi, Michael Chernick, mkt Sep 22 '18 at 18:32

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    $\begingroup$ It would seem to me that length of stay would require a different model than frequency of hospitalization, but that doesn't mean it couldn't be on the rhs of the regression. Why put it in as an offset, vs. as a standard rhs variable? Not sure, from a predictive point of view, that it's fair to include it at all, so depending on your objectives you might want to leave it out after all. $\endgroup$ – jbowman Jun 21 '12 at 0:12
  • $\begingroup$ It does'nt seem like total length of stay is a measure of exposure, it is more of an alternative response variable, maybe you could considere a joint model? A measurement of exposure would be total time under observation, if that is the same for all patients, there is no need to include it. $\endgroup$ – kjetil b halvorsen Sep 16 '17 at 20:51
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It doesn't seem like total length of stay is a measure of exposure (If for no other reason: when you are in a hospital bed, you are not under risk for being hospitalized!), it is more of an alternative response variable.

Maybe you could consider a joint model? A measurement of exposure would be total time under observation, if that is the same for all patients, there is no need to include it.

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