How should clustering be accounted for in logistic regression, when there are very few clusters?

I have survey data from 1000 patients. This is a convenience venue-based sample. In a specific city, at 9 hospitals that happen to have a psychosocial program, patients can opt into the program if they want and complete this survey.

I am conducting a logistic regression on this data modeling whether patients report financial difficulty (binary outcome). Independent variables include a mix of demographic and clinical variables.

I would like to account for clustering within each site, since survey data at each hospital will likely share characteristics (because sites vary in treatments offered, demographics of surrounding geographic catchment areas, staff data collection practices, etc.). The "effect" of the site is not of theoretical interest - it is mostly a nuisance that I want to account for.

• With only 9 clusters, the vce(cluster site) option in Stata adjusting SEs for clustering is inappropriate. Regular SEs were recommended over cluster-adjusted SEs.
• I've also read that multilevel modeling with <10 clusters will likely be underpowered and is not recommended (though I'm not sure if this extends to logistic regression or only applies to multilevel models with continuous outcomes).
• I've seen other options proposed, but all in the context of OLS/linear models.

Would it be sufficient to just include hospital site as a control variable in the model? What is the best option to do this in my case of LOGISTIC regression and FEW clusters? (Or the least bad option?)

• Clustering and regression are two different things, your terminology is confusing. This looks like a job for a multilevel / hierarchical model, where the hospitals are the random effect. What do you mean by with <10 clusters will likely be underpowered and what is this source? – user2974951 Jan 9 at 8:05
• To clarify: I am NOT saying I'm conducting a cluster analysis. I am conducting logistic regression on clustered data, and want to account for the fact that observations will likely have intra-cluster correlations by survey site. – xdrenched Jan 9 at 16:36
• Sources recommending against multilevel modeling with few clusters: 1) ctsi.ucla.edu/education/files/view/training/docs/… (p9) "If the number of sites is small (typically less than ten), then it is difficult to have the power at Level II to model many covariates" 2) bristol.ac.uk/cmm/learning/multilevel-models/samples.html 3) curranbauer.org/many-clusters-need-fit-multilevel-model Thanks! – xdrenched Jan 9 at 16:43
• @xdrenched: That quote talks about power to test hypothesis about level II, that is, the groups, in your case the hospitals. If you are only interested in the level I parameters, it is not relevant. – kjetil b halvorsen Jan 9 at 23:08
• Thanks for the clarification kjetil. Given that I'm only interested in level 1 parameters and only want to get rid of noise at the hospital level, does it make sense to use a multilevel/hierarchical model? Or is another option better? – xdrenched Jan 13 at 22:36