I have a data set with country aggregate patient data for yearly total number of diseases, treatments provided by health services, and some other covariates for two countries over 10 years. The disease variable is categorical with 10 different disease groups. For example 5000 patients had disease x in country 1, while 3000 patients had the same disease in country 2 in year 2010, and so on for other diseases and years.
I want to test for country differences in disease rates and trends over time, possibly adjusted for covariates. However, I am used to larger samples where I can adjust for clustering and repeated observations either by CSE or mixed models.
In this case, even though the total number of diseases add up to several millions (although not as individual data points), as far as I understand I still only have n=2 since there are two countries. Since the data set covers 10 years, I have a total of n*t=20 observations for each value. Given that both CSE and mixed models require approximately 30-50 groups or more (a discussion in itself), I am looking after some alternative statistical approaces.
I am a bit hesitant to proceed with regression approaches as I am not used to so small sample sizes with aggregated data, and I wonder whether some of you have input on relevant strategies.