I am running analysis on clinical data collected from patients which are correlated either by time (longitudinally) or more commonly different measurements of the same person at same time (eg. measuring variables of each eye).
My question is about accounting for this correlation when I running statistics, as the above violates independence of my observations.
I have come across mixed effect models which I have now read a great deal about and I think that's what I need. So I will include both eyes in any regression, but add the person as the random effect.
However reading more about this topic, there seem to "Cluster-correlated robust estimates of variance" (which is popular in STATA I believe), and multiple topics talking about "clustered standard error" or "hierarchical modelling" which frankly are bit out of my depth.
So my questions are:
When analyzing non-independent observations (eg. two eyes of same person) in regression, is mixed effect model the way to go? I have seen literature using clustered variance estimation. How is that different? (I'm using R for reference).
Mixed effect models are all regression based. How would I go about doing the equivalent of t-test or mann whitney u test while accounting for non-independence issue?