I have a large population of patients and hospitalization (>1 million) information. I'm trying to look at the relationships between various predictors and hospital re-admissions within 30 days. The data is set up as 1 record per hospitalization with a flag (binary outcome) yes/no if there was a repeat hospitalization following it. A "readmission" will also appear as its own record in the data set.
I'm attempting to use GEE models (logistic) to account for the fact that some individuals will contribute >1 hospitalization to the data set. I planned on attempting to use a exchangeable correlation structure as a starting point.
The issue is this: Everyone who contributes only a single record (approx. 50%) to the data will necessarily not have the outcome (i.e. they only had 1 hospitalization and therefore no re-admission). When I run a GEE with exchangeable correlation structure, it estimates the correlation as 0.9999, and often fails all together depending on my model (using SAS genmod). When I run it only within those with 2+ records, the estimated correlation is 0.6.
My question is: Can you use a GEE model when all clusters of size=1 have the same outcome value? What can be done?
Edit: The analysis I'm attempting is basically the same one as described in this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4581528/