I have count data by clinic (cluster) for which I would like to use generalized estimating equations to model the outcome. I was initially planning on using Poisson GEE, but checked if the data are overdispersed to determine if a negative binomial distribution should be used.

Overall, the outcome data were indeed overdispersed, so was planning to go with NB. However, when assessing clusters individually, some of the clusters had within-cluster data were not overdispersed (ie, Poisson distributed).

Should I use the overall distribution of the data to determine between Poisson or NB GEE models, or are there alternative approaches when distribution differences by cluster are present?