Figure 1.

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).