I haver performed a GWAS and I want to know if there are significantly more significant p-values than I would expect by random chance. Normally this is visualized with a QQ-plot but I want to have a p-value to support this claim. For that reason I am looking for a way to say that the observed and expected p-value distributions are significantly different. I only have access to summary data, so permutation tests are not possible.

Does anyone know of a method to do this test?

My take is using the Kolmogorov-Smirnoff test by using the observed and theoretical distribution. I am however, in doubt about how to properly define the theoretical p-value-distribution.

`p_exp <- runif(9e6, 1/9e6, 1)`

In this case there will approx. `alpha * N`

significant p-values, with significance threshold `alpha`

and `N`

tests.

I forgot to inlcude an important piece of information.... I only have access to summary data. Another and much more relevant reason to not do permutation.