I was recently discussing a study and I was presented with an interesting scenario.
In this hypothetical, there is a crossover RCT where all participants have pre-test values obtained on a physiological outcome variable (continuous) then a drug/placebo is administered for period of time and the participants return for a post-test (washout period and then the participants complete the other treatment condition drug/placebo). Now imagine there are two groups within the study (let’s just call them A & B). The groups A & B naturally differ on the outcome variable (pre-test differences are expected) and there is reason to believe that group A may have a different response to the drug. The research question here would be this: does group (A & B) moderate the response to treatment (drug). So overall, the theoretical study can be thought of as a 2 x 2 design (treatment x group) with pre & post values in every subject being obtained twice (placebo and drug conditions). In all my reading on the topic (which is limited), this would make the “ANCOVA” approach biased because these two groups already differ on the outcome variable, but the change score approach doesn’t seem appropriate either (maybe I’m overthinking this).
So what do all think: how would you approach analyzing this data and why?
(I also realize there are some related threads here, but thought this particular scenario was unique.)