We investigated whether trans-eVariants were each associated with numerous target genes, which may reflect broad effects of regulatory loci, as have been reported in model organisms5,28. Disambiguating true broad regulatory effects from artefacts remains an important challenge29. In our primary analysis, we applied aggressive correction of potential confounders, controlling for 15–35 probabilistic estimation of expression residuals (PEER) factors12 capturing 59–78% of total variance in gene expression levels (Supplementary Information 5). However, PEER and related approaches30 may also remove variance in gene expression levels arising from regulatory pathways and broad trans effects. Indeed, several loci with numerous associations were found in uncorrected data, but disappeared after controlling for PEER factors (Supplementary Fig. 13). Associations found in uncorrected data are likely to include many false positives for three reasons: 1) the PEER factors were strongly associated with known technical confounders (Extended Data Fig. 1 and Supplementary Figs 8, 9); 2) trans-eVariants identified from raw data and lost after correction were enriched for association with technical covariates (Supplementary Fig. 14); and 3) no other parameter setting clearly optimized trans-eQTL discovery (Supplementary Fig. 12).
