**Approaches for genetic marker-based causal inference**. Here we contrast different approaches for causality testing based on genetic markers. (a) single marker edge orienting involving a candidate pleiotropic anchor (CPA)

*M*. The upper half of (a) shows the starting point of network edge orienting based on a single genetic marker

*M *which is associated with traits

*A *and

*B*. The undirected edge between

*A *and

*B *indicates a significant correlation

*cor*(

*A*,

*B*) between the two traits. The causal model in the lower half of (a) implies the following relationship between the correlation coefficients

*cor*(

*M*,

*B*) =

*cor*(

*M*,

*A*) ×

*cor*(

*A*,

*B*). Further it implies that the absolute value of the correlations |

*cor*(

*M*,

*A*)| and |

*cor*(

*M*,

*B*)| are high whereas the partial correlation |

*cor*(

*M*,

*B*|

*A*)| (Eq. 1) is low. Figure (b) generalizes the single marker situation to the case of multiple genetic markers

. In this case, it is straightforward to generalize single edge orienting scores to multi-marker scores. Figure (c) describes a situation when a set of genetic markers

is also available for trait

*B*. We refer to the

*M*_{B }markers as orthogonal causal anchors (OCA) since

is expected to be 0 under the causal model

*M*_{A }→

*A *→

*B *→

*M*_{B}, the correlation. Using simulation studies, we find that edge scores based on OCAs can be more powerful than those based on CPAs (see Additional File 1).

## PubMed Commons