I have data with a binary outcome (success/failure) and a binary explanatory variable (treatment/control). For each subject (this is a clinical study), I have two observations, coming from two eyes. Obviously, the observations are correlated within a subject. I wonder if I should use GLMM or GEE to compare the two groups and to calculate the probability of success in each group. I wanted to ask what you think. I know the basic theoretical differences (that GLMM estimates a regression for each subject and GEE averages them all), yet I wanted to ask if anyone can specify the similarities (most of the time I get similar proportions), and the differences. How do you choose a model ? Based on what ?
Both of the models can be the correct approach. Both of them can deal with non-Gaussian distribution of the outcome variable and both can deal with the dependency (within subject) in your data. The important question would be: what specific research question are you aiming to answer? In an experimental design the individual subjects might be of interest. In that case a GLMM is preferred since it leads to an interpretation for individual subjects. If you are interested in the overall effect on the population a GEE is the model of choice, since it leads to an interpretation of regression coefficients for the population.