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
MB markers as orthogonal causal anchors (OCA) since

is expected to be 0 under the causal model
MA →
A →
B →
MB, 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).