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Figure 1 | BMC Systems Biology

Figure 1

From: Using genetic markers to orient the edges in quantitative trait networks: The NEO software

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 M A = { M A ( 1 ) , M A ( 2 ) , ... } MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdgeabbqabaGccqGH9aqpcqGG7bWEcqWGnbqtdaqhaaWcbaGaemyqaeeabaGaeiikaGIaeGymaeJaeiykaKcaaOGaeiilaWIaemyta00aa0baaSqaaiabdgeabbqaaiabcIcaOiabikdaYiabcMcaPaaakiabcYcaSiabc6caUiabc6caUiabc6caUiabc2ha9baa@40BB@ . 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 M B = { M B ( 1 ) , M B ( 2 ) , ... } MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdkeacbqabaGccqGH9aqpcqGG7bWEcqWGnbqtdaqhaaWcbaGaemOqaieabaGaeiikaGIaeGymaeJaeiykaKcaaOGaeiilaWIaemyta00aa0baaSqaaiabdkeacbqaaiabcIcaOiabikdaYiabcMcaPaaakiabcYcaSiabc6caUiabc6caUiabc6caUiabc2ha9baa@40C1@ is also available for trait B. We refer to the M B markers as orthogonal causal anchors (OCA) since c o r ( A , M B ( j ) ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4yamMaem4Ba8MaemOCaiNaeiikaGIaemyqaeKaeiilaWIaemyta00aa0baaSqaaiabdkeacbqaaiabcIcaOiabdQgaQjabcMcaPaaakiabcMcaPaaa@390B@ 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).

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