We conducted cis-eQTL mapping within the 44 tissues with at least 70 samples each. Only genes with ten or more donors with expression estimates > 0.1 RPKM and an aligned read count of six or more within each tissue were considered significantly expressed and used for cis-eQTL mapping. Within each tissue, the distribution of RPKMs in each sample was quantile-transformed using the average empirical distribution observed across all samples. Expression measurements for each gene in each tissue were subsequently transformed to the quantiles of the standard normal distribution. The effects of unobserved confounding variables on gene expression were quantified with PEER12, run independently for each tissue. Fifteen PEER factors were identified for tissues with fewer than 150 samples; 30 for tissues with sample sizes between 150 and 250; and 35 for tissues with more than 250 tissues. The covariates that were most consistently associated with PEER factors include factors related to parameters of donor death, ischaemic time, RIN and sequencing quality control metrics. In addition, we have observed that little, if any, genetic signal is present in the PEER factors (Supplementary Information 6).