models to explain the joint association of $E$ to $A$ and $B$:

1.  $E\rightarrow A\rightarrow B$: the association of $E$ to $B$ is indirect and due to a causal interaction from $A$ to $B$.

2.  $E\rightarrow B\rightarrow A$: idem with the roles of $A$ and $B$ reversed.

3.  $A\leftarrow E\rightarrow B$: $A$ and $B$ are independently associated to $E$.

To determine if gene $A$ mediates the effect of SNP $E$ on gene $B$ (model 1), one can test whether conditioning on $A$ abolishes the correlation between $E$ and $B$, using the partial correlation coefficient $$\begin{aligned}
  {\mathrm{cor}(E,B\mid A)} =
  \frac{{\mathrm{cor}(E,B)}-{\mathrm{cor}(E,A)}{\mathrm{cor}(B,A)}}{\sqrt{(1-{\mathrm{cor}(E,A)}^2)(1-{\mathrm{cor}(B,A)}^2)}.} \end{aligned}$$ If model 1 is correct, then ${\mathrm{cor}(E,B\mid A)}$ is expected to be zero, and this can be tested for example using Fisher’s $Z$ transform to assess the significance of a sample correlation coefficient. The same approach can be used to test model 2, and if neither is significant, it is concluded that no inference on the causal direction between $A$ and $B$ can be made (using SNP $E$), i.e. that model 3 is correct. For more details, see [@aten2008using], who have implemented this approach in the **NEO** software (<http://labs.genetics.ucla.edu/horvath/htdocs/aten/NEO/>).

Other approaches are based on the same principle, but use statistical 