I'm analysing the data for a cluster randomized study. There are 66 clusters randomly divided into two study arms: control and intervention, 33 clusters each. In total there are 2098 patients. The control ended up with 1038 patients and the intervention with 1060 patients. In tabular form my data looks like:
I need to compare the two arms and see if there's a significant difference between them. For a categorical variables such as marital status, I am using the cluster adjusted chi-square test (clchi2) on STATA.
My question is, which test should I use for the continuous variable age, seeing as the Mann-Whitney test doesn't work due to the clustering? Searching online points to using a model like GEE but how would I know the link function, correlation structure and distribution family to use?
Another approach I thought of would be to calculate the mean age of each of the 66 clusters then analyse for a difference of cluster means between the arms using the Mann-Whitney test. It's crude, but is it correct?