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Schematic representation of the MR2 model, which allows the exploration of the model space consisting of all possible subsets of exposures (bottom gray circle) directly associated with the responses (top gray circle) while estimating the residual correlation between the responses (top gray circle) and vice versa. Model depicted in (A) is reported in MR2 as follows: X1 is a shared exposure for outcomes Y1 and Y3, while X2 has a distinct direct causal effect on Y2 (directed edge). Residual dependence between Y1 and Y2 is still present after conditioning on the associated exposures (undirected edge), and it depends on the unmeasured pleiotropic pathway A.
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