Fig. 6: A graphical illustration for the Slope-Hunter approach.
From: A robust method for collider bias correction in conditional genome-wide association studies
Slope-Hunter is applied on estimates of SNP association coefficients with a quantitative trait (I), \({\hat{\beta }}_{GI}\), and a quantitative outcome (P) conditional on I, \({\hat{\beta }}_{GP}^{\prime}\) that are simulated for 10,000 independent SNPs from a dataset of 20,000 individuals, with: (a) no genetic correlation between SNP effects on I and P; (c) correlated genetic effects on I and P. In both input datasets, depicted in (a) and (c), the SNP associations are simulated under a hypothesised four-component model for effect-size distribution in which 5% of SNPs have effects on I only, 5% on P only, 5% on both and 85% on neither. The heritability of I and P is 50% and the non-genetic common factors explain 40% of variation in both I and P. The fitted correction factors estimated using the Slope-Hunter (SH) method are shown in (b) and (d) for the input data in (a) and (c), respectively. After excluding the SNPs that are not associated with I, using a p-value threshold (p > 0.001), the SH method identifies the cluster of variants affecting I only (GI., depicted in red points) and the cluster affecting both I and P (GIP, depicted in grey points). The true and estimated correction factors using the SH and the `Hedges-Olkin' estimator of the Dudbridge et al. (DHO)7 methods are represented by the slopes of the solid black, dashed red and dashed blue lines, respectively. These slopes are −0.383, −0.388 and −0.349 in (b) and −0.460, −0.458 and −0.273 in (d) for the true, SH and DHO estimators, respectively. Source data are provided as a Source Data file.
