Fig. 1

GNet-LMM model illustration and basic simulation experiment. a Graphical model representation of the GNet-LMM algorithm. For each SNP A–gene C trans association test, GNet-LMM identifies and conditions on exogenous genes with incoming edges (green, Gene B) but not on genes with outgoing edges (red, Gene D). Exogenous genes either tag confounding sources of variation (Conf) or regulatory effects between genes. To define exogenous genes, GNet-LMM tests for V-structures gene A - > gene C < - gene B (blue box) that are linked to SNP A via gene A. b True positive versus false positive rate when considering alternative methods applied to 1000 synthetic eQTL datasets that were simulated assuming a regulatory structure as in (a). Shown are results obtained from standard LMM without conditioning (LMM), an LMM that exclusively conditions on true exogenous genes (gene B, Ideal-LMM), an LMM that conditions on co-regulated genes (gene D, coreg-LMM) and the GNet-LMM algorithm that uses the V-structure approach to determine the set of exogenous genes for conditioning