I am working on an instrumental variable application using clinical data. We will use a so-called preference-based instrument. We may include this as a continuous variable. With a continous instrument, we can obtain the average marginal treatment effect (AMTE). I am having some trouble translating this from the standard econometrics jargon to a clinically relevant formulation that clinicians may find meaningful and intuitive.
I've seen several formulations, but they all rely on understanding the specific use of "marginal" in this context. I have studied economics, and I'm used to thinking of the marginal effect as the change in outcome given a one unit change in the independent variable. (In statistics, I know it can refer to the unconditional mean.) However, in the context of AMTE with a continuous instrument, categorical treatment and outcome, I am unsure how it can be described in more layman terms. I've seen several formulations, e.g.
- "This is the effect of a treatment on the marginal individual entering treatment" (Meghir, 2009)
- MTE is "...the difference between the treated potential outcome and the untreated potential outcome for an individual marginal to selecting into treatment ... " (Kowalski, 2016)
- "MTE is therefore defined as a continuum of treatment effects along the full distribution of $U_{D}$ (the individual unobserved characteristic that drives treatment decisions)." (Cornelissen et al., 2016)
- By this description, local IV curves seem to be related or synonymous: "local IV (LIV) curves, i.e. effects among units who would comply right at a given threshold value of the instrument." (Kennedy et al. 2018)
I'll add that there is at least one more seemingly related post that goes into average and marginal treatment effect. I think Meghir's formulation could be what I'm after, but it hinges on understanding "the marginal individual".
