I am an epidemiologist trying to understand GEEs in order to properly analyze a cohort study (using Poisson regression with a log link, to estimate Relative Risk). I have a few questions about the "working correlation" that I would like someone more knowledgable to clarify:

(1) If I have repeated measurements in the same individual, is it usually most reasonable to assume an exchangeable structure? (Or an autoregressive if measurements show a trend)? What about independence - are there any cases where one could assume independence for measurements in the same individual?

(2) Is there any (reasonably simple) way to assess the proper structure by examining the data?

(3) I noticed that, when choosing an independence structure, I get the same point estimates (but lower standard errors) as when running a simple Poisson regression (using R, function `glm()` and `geeglm()` from package `geepack`). Why is this happening? I understand that with GEEs you estimate a population-averaged model (in contrast to subject-specific) so you should get the same point estimates only in the linear regression case.

(4) If my cohort is at multiple location sites (but one measurement per individual), should I choose an independence or an exchangeable working correlation, and why? I mean, individuals in each site are still independent from each other, right?? Thus for a subject-specific model, for example, I would specify the site as a random effect. With GEE however, independence and exchangeable give different estimates and I am not sure which one is better in terms of underlying assumptions.

(5) Can GEE handle a 2-level hierarchical clustering, i.e. a multi-site cohort with repeated measures per individual? If yes, what should I specify as a clustering variable in `geeglm()` and what should be the working correlation if one assumes for example "independence" for the first level (site) and "exchangeable" or "autoregressive" for the second level (individual)?

I understand these are quite a few questions, and some of them may be fairly basic, but still very difficult for me (and maybe other novices?) to grasp. So, any help is greatly and sincerely appreciated, and to show this I have started a bounty.