These assumptions imply that the genetic variant should not have an effect on the outcome except via the risk factor. Under linearity assumptions, the association between the genetic variant and the outcome can be decomposed into an indirect effect via the risk factor and a direct effect: (1)βYj=αj+θβXj, where θ is the causal effect of the risk factor on the outcome. Genetic variant j is pleiotropic if α j≠0, and α j is the direct effect of the genetic variant on the outcome. Figure 1 contains a direct effect α j via an independent pathway, which violates the IV3 assumption.
