Fig. 3

Detailed runtime and AUPRC comparison of the selected representative methods (Table 1) in Simulation Design 2. Each point represents the average across simulated data sets. The x-axes are: number of effect SNPs per gene (numOfEffectSNPs), number of simulated covariates (numOfCovariates; including known and hidden covariates), proportion of variance explained by genotype (PVEGenotype), and proportion of variance explained by covariates (PVECovariates) (Additional file 1: Section S3). a PCA and HCP are orders of magnitude faster than SVA, which in turn is orders of magnitude faster than PEER. b PCA outperforms SVA, PEER, and HCP in terms of AUPRC across different simulation settings. For ease of visualization, the y-axis displays \(\left( \text {AUPRC}-\text {AUPRC}_\text {Ideal}\right) /\text {AUPRC}_\text {Ideal}\). Consistent with our expectation, the performance gap between Unadjusted and Ideal is the largest (and thus accounting for hidden covariates is the most important) when numOfCovariates is small, when PVEGenotype is small, and when PVECovariates is large