Fig. 5: Scatter plots for simulated estimates of SNP association with a quantitative trait (I), \({\hat{\beta }}_{GI}\), and a quantitative outcome (P) conditional on I, \({\hat{\beta}}{\,\!}_{GP}^{\prime}\).
From: A robust method for collider bias correction in conditional genome-wide association studies
The estimates 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; (b) correlated genetic effects on I and P (correlation coefficient = 0.4). In both analyses, (a) and (b), 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 analyses in both (a) and (b) induced collider bias due to the common causes of I and P, including common polygenic effect as well as non-genetic common factors. The true collider biases are represented by slopes of the black solid lines, which are −0.383 and −0.460 in (a) and (b), respectively, while the estimated correction factors using the `Hedges-Olkin' estimator of the Dudbridge et al. (DHO) method7 are represented by slopes of the blue dashed lines, which are −0.349 and −0.273 in (a) and (b), respectively. The analysis depicted in (b) illustrates potential inadequate correction using the DHO method when the `InCLUDE' assumption (Index Coefficient Linearly Uncorrelated with Direct Effect) is violated. Source data are provided as a Source Data file.
