In order to increase the number of detectable cis- and trans-eQTLs we applied a principal component analysis (PCA) on the sample correlation matrix. We, among others [19], [20], argue that the dominant PCs, capturing the larger part of the total variation, will primarily capture sample differences in expression that reflect physiological or environmental variation as well as systematic experimental variation (e.g. batch and technical effects). Figure S6 shows for the 1,240 HT12 samples what per individual the PC scores are. It is evident there are, especially among the first PCs, strong batch effects are still present after proper quantile-quantile normalization. By removing the variation captured by these PCs, we expected that the residual expression is more strongly determined by genetic variants and the number of significantly detected cis- and trans-eQTLs will increase. An aspect to consider is that with the removal of more PCs from the data, the degrees of freedom of the data will decrease. Furthermore, it is not immediately clear which PCs will actually capture physiological, environmental, and systematic variation, which might lead to removal of genetically determined
