I have # of students consenting to be vaccinated and # of students eligible to be vaccinated for 77 schools in three school years (2010/11, 2011/12, and 2012/13). Between 2011/12 and 2012/13 there was an intervention to increase consent rates. I want to be able to model (with a repeated measures model) the change in consent rates over time.
First, I am having trouble deciding what distribution the outcome is since it is at the school level and not the individual-level. It's not a simple 1-consent, 0 - no consent as schools contribute multiple counts of #consents and #eligible. It's a rate but does not really follow a poisson distribution.
Question 1 - is an aggregrate rate across schools, say in 2010/11, just the mean of individual school rates (to me this doesn't make sense) or the sum of #consents/sum of #eligible across all schools? If it's the latter, do I use a binomial or poisson distribution to calculate CIs, or does it matter?
Question 2 - Since I don't have student level data, does it make sense to use GEE with the poisson family and log-link? This would be using count data of #consents per school and offset of #eligible by school. Schools in this sense would be the "subjects". I would model the pre and post-intervention time periods separately.
Any insight is greatly appreciated!