I have been reading about causal mediation analysis in settings where there is time-varying confounding of the mediator-outcome relationship. The estimands in question are the randomized analogues of the natural direct/indirect effects where Ma (the counterfactual values of the mediator under treatment a) is replaced with Ga|C, where Ga|C is a random draw from the distribution of the mediator under treatment a conditional on covariates. To my knowledge this type of estimands were originally proposed in this paper: https://journals.lww.com/epidem/fulltext/2014/03000/effect_decomposition_in_the_presence_of_an.22.aspx

Specifically, I've been looking at the following papers detailing:

  1. a marginal structural model approach: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5560424/
  2. a parametric g-formula approach: https://pubmed.ncbi.nlm.nih.gov/27984420/
  3. software implementation: https://pubmed.ncbi.nlm.nih.gov/34028370/ - detail of estimation at https://bs1125.github.io/CMAverse/articles/overview.html#confounders-affected-by-the-exposure-1

My question is about a step in the g-formula approach that I don't understand - specifically step 2b in the g-formula paper (p270) or step 5 in the g-formula approach on the cmaverse page, where the simulated values of the mediator are randomly permuted. If I understand correctly, this means that the N simulated values of the mediator are randomly reassigned to different sample members. The same step is absent from the MSM approach, which simply uses the simulated values of the mediator.

The thing I don't understand is why it is necessary to randomly permute the simulated values, which are already a random draw from the modelled distribution of the mediator conditional on covariates. Does this not also break the 'conditional on covariates' bit of the original definition?



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