I have a population of 200,000+ patients and their hospital visit information. I'm trying to see if having a certain disease would have an effect on whether they will have readmission or not (this is the binary response variable). Since each patient can have from 0 to up to 200 visits, I consider each visit as repeated measures, and visits from the same patient form a cluster. Naturally, I have a large number of clusters, and varying cluster sizes. For the $i$th cluster, the cluster size is $T_i$. I prefer using GEE instead of GLMM since I'm looking at the population instead of individuals.
My question is, how does GEE treat the nuisance variable $t$ $(t = 1, 2, ..., T)$, where the size $T$ of each cluster varies?
Can the different $T$ be regarded as missing values? Agresti (Categorical Data Analysis, 3rd edition, Page 472) mentioned that, for a GEE model, the missingness can only be ignored if the they are MCAR (missing completely at random). I don't think this is the case here, since the number of visits from each patient is clearly correlated with the patient's health conditions. Also the lag between hospital visits is different for different patients.
Some studies have suggested that GEE can be directly applied when cluster size varies, especially studies that are not in the context of longitudinal studies, where a cluster is a neighborhood, hospital, etc. So is the handling of different cluster sizes something that comes naturally in the process of GEE? If so, at which step is it dealt with? For example, is it dealt with when we are estimating the covariance structure? If it is something that needs to be especially addressed, then how can I do it?