findings: (1) For the nicotine symptoms, the p-values fall on the diagonal line and this indicates that there is no SNP associated with nicotine symptoms; (2) For the symptoms of the other three substances, all the p-values deviate from the diagonal lines (except for 0 and 1), with the p-values of alcohol symptoms furthest away from the diagonal line and the p-values of the remaining two symptoms closer to the diagonal line. Since the four symptomatology variables are moderately correlated and they all measure the common construct of addiction, we used them as the multivariate phenotype and applied the proposed Fisher combination approach (FC-Kendall) to identify the SNPs associated with it. The QQ-plot of the p-values for this multivariate analysis is shown in Fig. 4 indicating that some SNPs are associated with addiction across substances.
