Encouraged by the low FDR of our PC-adjusted analysis, we used a sequential search to determine the number of PC that maximized power (Supplemental Fig. 1; Liang et al. 2009). The number of genes mapped locally (LOD > 6 or P < 1.5 × 10−7, the threshold we previously used to define genome-wide significance in the same data set) (Dixon et al. 2007) was used as an indicator of power. In the MRCA data set, as we gradually included additional PCs in the model, the number of local eQTLs (autosomes plus chromosome X) increased gradually from 2175 (with no PCs) to 6238 (when 69 PCs were used to control for nongenetic variation). Further increases in the number of PCs led to decreases in the number of eQTLs detected (and likely power). This eventual decrease in power may be explained because the later PCs are dominated by contributions from a few transcripts. The optimal number of PCs seems to vary by sample (e.g., 61 for the MRCE panel) and can be estimated in other data by using a similar procedure to that used here (Supplemental Fig. 1).
