Hierarchical modeling in a pre-post study

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We are conducting a study which has a pre-post design. The unit of the study is the outpatient visit. In each visit, we study how patients and physicians interact.

Each physician will see between 3-6 patients and most of these patients (ie, except for dropouts) will be seen twice: once in the pre-phase, once in the post-phase.

Because the relation of patient to physician in any given visit is symmetric, it would seem to lead to two distinct ways to model the hierarchical structure. Starting from the root vertex of the (directed) tree:

A) study → physician → patient → pre/post

B) study → pre/post → physician → patient

Is there a scientific reason or stat. methodological issues to prefer one nesting over the other? What differences in results can we expect?

Any pointers to the literature are appreciated.

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关键词：Hierarchical Modeling model study ARCH structure patients relation between design

Yes, there is a good reason to prefer (A) over (B).

(A) correctly reflects the design of the study, while (B) does not. The two models are not equivalent, and the choice is not arbitrary.

Model (B) posits that Physicians are nested under Pre/post, as are Patients (by virtue of being nested under Physicians), but clearly neither of these is true. To say that Physicians are nested under Pre/post would be to say that each Physician is observed under one and only one level of Pre/post... that is, we have some Physicians that are "Pre Physicians", and other Physicians that are "Post Physicians", but no Physician has both Pre and Post observations (according to model B).

But in actual fact, each Physician does have some Pre observations and some Post observations. And because the Pre/post observations under one Physician are different from the Pre/post observations under another Physician, we can see that the order of nesting is actually the reverse... Pre/post is nested under Physician, not vice versa. And of course, Patients are in the middle of this hierarchy.

The difference here is not merely conceptual. There are tangible statistical consequences that follow from the choice of (A) or (B). Perhaps most saliently in this case, in model (A) the denominator of the test for the Pre vs. Post difference is free of variance due to both Physician and Patient, because these are held constant when comparing Pre-scores to Post-scores. (This becomes slightly more complicated in the presence of unbalanced/missing data, but we'll ignore that for now.) In model (B), Physician and Patient variance are both (wrongly) thrown in the denominator for testing the Pre vs. Post difference. This is "wrong" in the sense that it leads to a test of the Pre vs. Post difference that is overly conservative.

I think you want to go for something along option A). Obviously, patients are nested within physicians, i.e. you want to account for the effect of physicians on your measurements. Finally, you are dealing with repeated measures on the patient level.

Approaching the multilevel/hierarchical modeling this way guarantees the correct shrinkage towards the appropriate levels of hierarchy. You want the individual time courses to tend towards the 'average' time course for this particular physician, which in turn shrinks toward the sample 'average'.