Throughout this paper, the approximation strategy is used because it runs fast for power simulations. Another reason for using the approximation strategy (rather than standard permutation with a stopping rule) is to produce Uniform(0,1) distributed p-values (under the null hypothesis; see Figure S2) for all the tests conducted, which is preferred if further analyses of the p-values are conducted in e.g. a pathway analysis. The standard permutation approach can only produce uniformly distributed p-values under the null hypothesis if no stopping rule is used, which is a computationally expensive approach.
