Relaxing Assumptions and Targeted Estimands with MOST

Very interesting, once again. My feeling is that we are mixing two elements : a local behavior (what happens for state 1) vs a global behavior (variograms, etc). I’d argue that global fit is what we would be interested in initially, with the reassuring element that our assumptions like PO across outcome levels can be grossly violated without altering at least some information (the direction of the treatment effect). So, to your point of adressing fit, I would not diverge from the global checks first. But if we are now looking at things locally, eg landmark probabilities in a specific state, then I think we need to be careful that the null is not a global null : there can be no effect for my state of interest while there is an effect for all other states that will ´contaminate’ my local effect if I’m not careful about that. If I recall, you had something similar in another study but in the reverse: only an effect in one state vs no effect in the other ones, so including the latter dilutes your capacity to detect what you are interested in if you allow in MOST for some structure across outcome values. I keep circling around this concern that what is appropriate globally may not be locally, so that we need to pay attention to the way we introduce MOST. If we are in a complex setting (eg rare disease) and we would already be thrilled to say ‘there is something’, then I would not think about being picky with local questions. But in other settings, my feeling is that we need to think about a principled way to use global structure whenever appropriate, while buying some protection when it is not for local questions (be it because it’s going to ´inflate´ alpha or dilute ´power’ - I know this is not sufficiently well-formulated, but I’m sure you’ll understand what I mean). As I wrote before, this is surely not only mathematical, as we need to have information about the disease process to be able to anticipate best whenever structure (borrowing across outcome values) may be appropriate. But I also anticipate we lack some methodological tools to do that best as well (in reference to the comment by Phil Boonstra mentionned earlier in this thread). What I lack most (MOST) are some case studies to refine this and make it concrete. More to follow soon hopefully