I am involved in the analysis of the effect of an intervention at five different hospitals. The intervention aimed to increase the use of a particular equipement when treeating a patient, so the outcome variable is binary (used the equipement/did not use the equipement). The study is not controlled, just pre- and post intervention measurements, with different patients before and after the intervention, so just two independent groups.
However, the hospitals are very different with different types of patients. To account for this clustering, I initally considered a logistic regression model with "equipement use" as an dependent variable and time (pre vs post) and hospital as independent fixed effect models, possibly with an interaction term. However, recently I have recieved a suggestion that a GEE would be a prefered choice instead of a logistic regression. I guess this person sees hospital as a random factor, and therefore would like me to consider an population-averaged effect (the population in this case being the hospitals). Does anyone have any thoughts on this? I don't see the advantage of this approach, but I get a feeling that I am missing something crucial. Are there any other suggestions for analysis?
The aim of the study is to examine the effect of the intervention, the hospitals per se are not of interest. They are just five convinience sampled hospitals, certainly not a random sample.