I'm learning about mediation analysis within the context of a randomized control trial. Let's assume a "vanilla" case: Perfect randomization, 100% compliance, zero SUTVA violations. Now, Suppose an experiment to test the effect of limes on scurvy, mediated by vitamin C.
The elements worth considering:
- Lime assignment indicator
- Vitamin C in a given lime
- Vitamin C in pre-ingestion bloodstream
- Vitamin C in post-ingestion bloodstream
- Scurvy indicator (or continuous measurement.)
We can condition on [1] treatment and [3] covariate without any problems; due to randomization, there is no selection bias and so conditioning on [3] amounts to CUPED, which should shrink standard errors around the effect estimate but not change the effect estimate, itself. Conditioning on [2] we cast the treatment as a continuous variable, with varying levels of exposure (to vitamin C through limes.)
Where things get complex is conditioning on [4], the post-ingestion bloodstream value of vitamin C; this is the mediator. If vitamin C is not the causal reducer of scurvy then reduced and elevated levels of [4], alike, will have similar outcome responses [5]. However, if [4] is indeed a mediator with a non-zero effect, then some portion of the treatment effect will be siphoned off from the [1] coefficient into the [4] coefficient.
We must tread carefully. While we can randomize [1], the treatment exposure, we cannot randomize [4] the mediator. For example, suppose that we want to perform block randomization; we can stratify on [3] because this value is known pre-treatment. However, we cannot stratify on [4] because we would already need to know the degree by which post-ingestion bloodstream vitamin C levels moves in response to the treatment, which is the inverse to the same question, "is the effect of limes on scurvy mediated by vitamin C?"
I have read that there are several methods used for mediation analysis. But all come with assumptions that are hard seldom hold.
So my questions are twofold:
- Do I have a proper understanding of the problem space (mediation analysis)?
- What are some of the most robust methods available to address?