I am estimating the global risk of infection risk in a population of patients, but these patients are clustered in hospitals and wards/departments. If I just take the crude prevalence (infected patients over the total), ignoring clusters, I get a certain value, around 8%.
If instead, I use an intercept-only model with a random intercept at the hospital level, I get a lower risk (~6%) which becomes even lower (5%) if you add another hierarchy, nesting wards into hospitals.
How should I describe these lower risks; should I say that it's a more robust estimate and I would see less variance if I repeat the study with a different selection of hospitals and wards? Are these estimates also more robust in the case of non-random sampling choosing of hospitals and wards (we have a convenience sample).
Note that the characteristic of the hospital (such the size) and the ward (such the specialty) do influence the risk. Furthermore, I noticed that taking the average of the per-hospital risks gives again a number around 6%.