The accuracy of the permutation test can be improved by noting that the minimum p-value, sum statistic and truncated product can all be regarded as the extreme value of a large number of observations [33]. Therefore, they should follow the extreme value distribution[43] and by fitting the parameters of the distribution to the values observed in permutation replicates, more accurate significance levels are obtained. Equivalently, fewer replicates are needed to reach a given accuracy. The efficiency gain depends upon a number of factors, including the true significance level and the number of tests, and it is difficult to compute standard errors for the empirical p-values. Nevertheless, this approach has the advantage of being generally applicable and, importantly, the fitted distribution can be re-used in subsequent tests of the same genes in the same population. This will be useful for studies based on a standard genome-wide marker panel [3], leading to substantial time savings over the long term.
