I ran Lasso for a trait given SNPs to get sparse regression coefficients. Then I ran a permutation test (ie running Lasso on shuffled datasets) to get the null distribution, and thus p-values for each regression coefficient. I now have created the QQ-plot for the p-values. Do these results show that there's genomic inflation that needs to be corrected?
On the one hand, the slope of the curve doesn't look good. On the other hand, (and this isn't apparent from the plot), the vast majority of coefficients (> 90%) were non-zero, and thus have p-values of 1. So the SNPs in the curve are actually atypical coefficients. This also means that if I try to do genomic control, the median lambda_gc is actually 0, which would indicate deflated p-values! Is there another way to assess p-values for confounding when doing sparse regression for GWAS?