Fig. 4

Inference of the causal effects of DNA methylation on gene regulation. a Representation of a simulated scenario, with the three varying parameters (α, β, and τ). b Comparison of the mediation analysis (med) with a partial correlation approach (PartCor) using a range of different simulated parameters for α (0.3–0.8), β (0.9–0.1), and τ (0.1–0.9). Note that the parameter range simulated for β and τ was adjusted so that we kept 75% of the variance unexplained (random noise parameter γ = 0.25). The difference of the area under the curve (AUC) between the two approaches is represented with different shades of red and blue. The sizes of the circles are proportional to the mean AUC of the two approaches. Two examples of the ROC curves are shown in the upper part of the figure. c Number of mediated and non-mediated eQTM-genes for negative and positive associations between DNA methylation and gene expression. The percentages of these two categories are also indicated. d Proportion of variance of gene expression explained by DNA methylation (light gray) and genetics (dark gray), in mediated and non-mediated cases