# Poisson model with multiple time offsets

I am trying to model health outcome rates by flu-season. I.e. hospitalization rates in good flu-years versus bad years. I am working with individual level nursing home resident data from administrative claims across several flu-seasons. The model can take some general form like so:

$Y_{isf} = FluSeason_{s} + X_{i} + a_{f}$

Where $X_{i}$ are ID-covariates and $a_{f}$ are facility fixed effects.

One issue here is that flu-season is varying exposure by person. So only a few days versus resident for the whole season.

To model this I was thinking about a Poisson model offset for flu-season exposure like so:

$Log(Y_{isf}) = Log(season\;exp) + FluSeason_{s} + X_{i} + a_{f}$

My problem with this is that each individual has varying exposure for each season, while above I am looking at total seasonal exposure. However, I view flu seasons as having varying effects because of epidemics etc., with each flu season exposure needing to be accounted for. I haven't heard of someone doing multiple offsets or if that's possible. I was thinking about creating three separate cohorts for each season offset for time in that season and comparing rates.

My question: Is there a way to keep a everything in one model but can account for this variable exposure time for each season? I was thinking maybe a more advanced hierarchical model.

• An offset is just a constant term included in the linear predictor, so if you have multiple offsets, you can just sum them before including the sum in the model. – kjetil b halvorsen Sep 17 '17 at 13:13