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I have a large data set where we have 5 calendar years data for each person, and we have information about the number of outcomes (taking values 0,1,or 2) each year. We have to account for the fraction of the year the person was exposed. If this was descriptive, I could do # events / person-years to get an appropriate rate. However, the people are clustered within groups, and we have to adjust for both individual- and group-level covariates. So the approach I was going to take is multilevel modeling using a binomial GLMM to . However, I'd love suggestions on how to address the person-year accounting within the model, since I'm not sure how to do this in the binomial framework. I'm loathe to use a Poisson model since the number of potential counts is limited to {0,1,2}. I should note that over the 5 years (or really over a lifetime) the person could not have more than 2 outcomes.

Bonus points for providing suggestions using SAS (maybe GLIMMIX), since that is a constraint of my computing environment that is unfortunately non-negotiable.

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Binomial seems wrong, because >1 event is possible. Poisson or Negative Binomial with a log-exposure offset (and a random effect across years too account for the across year coronation) also seems wrong, as you say, because at most 2 events are posdible. Should time after event 2 for a year still be counted as exposure time at risk?

In any case, assuming at most 2 events in a time period, a truncated Poisson (or Negative Binomial) likelihood (i.e. just the pmf terms for 0, 1 and 2 re-normalised to sum to 1) using the summef up data across all the years would be an option. Everything else could then work the same like a usual Poisson model (log-link function, log-exposure offset etc.). Even if software does not have this available, one can still use functions/procedures that allow user-specified log-likelihood functions (e.g. PROC NLMIXED in SAS/STAT).

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  • $\begingroup$ Thanks. For the range of binomial probabilities empirically observed, the Poisson model is a pretty good approximation to the binomial, so we're going with a Poisson or Neg Binomial. $\endgroup$ – Abhijit Apr 1 '18 at 0:01

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