Then, we checked whether the null P-values coming from permutations are beta distributed again in the GEUV_EUR dataset. To do so, we (1) stored for each phenotype the best P-values obtained from 1000 permutations as observations, (2) estimated k and n by ML from the 1000 resulting P-values, (3) simulated 1000 P-values from the newly parameterized beta distribution as expectations and (4) compared both observations and expectations to assess their goodness-of-fit visually (QQ-plots) and statistically (one sample Kolmogorov–Smirnov test). Overall, we find very high degrees of concordance between results; both when pooling all genes together (Fig. 1d) and also when looking at each gene individually (Fig. 1e).
