Causal not confounded gene networks: Inferring acyclic and non-acyclic gene Bayesian networks in mRNA expression studies using recursive V-structures, genetic variation, and orthogonal causal anchor structural equation models

To improve the recovery of gene-gene and marker-gene interaction networks from microarray and genetic data, we first propose a new procedure for learning Bayesian networks. This algorithm, termed Bilayer Verification, starts with a user-specified leaf node, and then searches upstream to locate portions of the biological interaction network that can be verified as un-confounded by hidden variables such as protein levels.;Estimates of the specificity of the algorithm are made through small sample simulation, and an illustrative network is learned from mouse microarray data that implicates particular liver genes in the Apoe null mouse model of diet-induced atherosclerosis.;We next extend these algorithms by exploring how multiple independent causal anchors that impact the same trait can be used to organize gene expression data into non-acyclic gene-trait causal networks. While earlier methods begin with sets of single pleiotropic QTL, we formulate a gene network recovery approach based on a synthesis of (1) Bilayer verification theory; (2) selecting orthogonal causal anchors (independent Quantitative Trait Loci (QTL) MA and MB that show asymmetric MA → A → B ← MB impact on traits A and B; abbreviated OCA); (3) Structural Equation Model comparison; and (4) forward-stepwise regression. Combining these, we introduce a family of Local-structure Edge Orienting (LEO) scoring algorithms that generate model-comparison metrics. LEO scores weigh the evidence for competing causal graphs using local models that isolate each A → B edge evaluation from its neighbors to prevent error propagation and relax the constraint of network acyclicity.;Our studies show that the OCA-based LEO scores have almost twice the detection power at comparable false positive rates compared to single QTL and common pleiotropy anchor models in the face of confounded association. Moreover if we match thresholds to obtain comparable power, the orthomarker methods obtain better false positive rates than competing methods.;We demonstrate the method by recovering multiple positive controls in the cholesterol biosynthesis pathway and implicating four novel genes as being downstream and hence co-regulated by the sterol regulatory pathway in mouse liver: Tlcd1, Slc25a44, Slc23a1 , and Qdpr.