Because of the negative consequence of the independence assumption, it is desirable to conduct the Fisher combination test without the assumption. Ideally, we could calculate the exact p-value of the T statistic in Eq. (1) using the permutation method, which does not require the unrealistic assumption and also controls for the type I error [26]. Yet, the permutation method is a very time-consuming procedure, particularly in a genome-wide context. Thus, an improvement in computational efficiency is warranted.
