A partial correlation is the correlation between X and Y conditioned on one or more control variables. In this study, first order partial correlation was used to detect the interaction between trans-regulated transcripts and cis-regulated candidate genes conditioned on the genotype (marker rs8242481 at 175.058 Mb). If x, y and z are trans-regulated transcripts, cis-regulated transcript, and genotype in the QTL, respectively, then the first order partial correlation coefficient is calculated as—where rxy can be either Pearson correlation or Spearman's rank correlation between x and y. We employed the Spearman's rank correlation because the expression levels of many transcripts do not follow a normal distribution.
