Fig. 3

Performance on simulated datasets across varying density and strength of the confounding signals. Average false discovery proportions (A) and true positive rates (B) are compared at 5% FDR using simulated datasets. 1dFDR-U and 1dFDR-A represent the one-dimensional FDR control procedures based on the unadjusted model and confounder-adjusted model, respectively. 1dFDA-H is a heuristic adaptive procedure that uses the adjusted or unadjusted model depending on whether the confounder effect is significant (nominal p value < 0.05). The density of the true signals is 10%, and the strength is moderate. The performance is evaluated at varying confounding signal strength (left: weak, right: strong), confounding signal density (top: low, bottom: high), and the correlation between the variable of interest and the confounder (inside the panel, “+,” “++,” and “+++” represent a low, medium, and high correlation (ρ ≈ 0.2, 0.6, 0.8), respectively). 2dFDR maintains the FDR at the target level across settings and is significantly more powerful when the correlation between the variable of interest and the confounder is not low (++/+++). The power difference decreased as the confounding signals become denser (top to bottom)