# interactions for paired and unpaired proportions

I would like to compare the effect of a treatment between two groups.

My dataset is summarized in this table:

Each score corresponds to a proportion (namely, the proportion of successes on a given cognitive test).

How would you compare the difference of treatment effects between Group 1 and Group 2, taking into account the within-subject variability? Would you use a logistic regression?

Thanks a lot

If your interest is in overall test scores, rather than the individual answer probabilities, you probably want to consider your outcome variable $score_{\text{After}}-score_{\text{Before}}$. However, if you want to consider individual question probabilities nested within subjects within disease groups, you would want to explicitly model each question's paired difference separately (although it seems like different subjects had different numbers of tests… is there a missing information issue here?).