I evaluated the yield of a diagnostic intervention for the detection of heart failure in a cluster RCT (intervention vs usual care, 25 sites, 1200 patients, 1 year follow-up). For our main outcome, number of new diagnoses in each arm, I used GLMM with site added as a random effect and several covariates as fixed effects to account for potential clustering.

A secondary outcome is medication changes. I want to know whether patients in the intervention arm receive more evidence-based medication than those in the control arm (in other words: did the increase in diagnoses lead to an increase in treatment?) However, a simple chi square test at follow-up won't work, because there are slight differences in medication use on baseline due to the cluster-randomized design. How best to answer this question, then? GLMM or logistic regression for each type of medication separately? Or is there a simpler solution?

Many thanks in advance for your insights!