Fig. 1

Boxplots of the bias across simulation replications based on a two-step variable selection method, either the iterative SIS or FDR (simulation setting II). X-axis corresponds to the percentage of true mediators; Y-axis corresponds bias across simulation replications. A, B non-mediators \(\mathbf{M} ^{(2)}\) are included in addition to the true mediators; C, D non-mediators \(\mathbf{M} ^{(1)}\) are included in addition to the true mediators. Rsq (All):\(R^2_{Mediated}\) based on all the data without variable selection; Rsq(VS): \(R^2_{Mediated}\) based on the variables selected either by iterative SIS (A, C), or by FDR (B, D); Rsq (True): \(R^2_{Mediated}\) based on the true model/mediator set based on all the data. The numerical values and the bias and variance corresponding to the none mediators (null model) are available in Additional file 1: Tables S4 and S5