between expression and trait, see below) conditional on the observed GWAS statistics at the locus (which may not be drawn from the null of no association). The permutation test empirically computes this distribution of ZTWAS values conditional on the observed Z and asks how extreme is the observed ZTWAS among all possible W coming from permuted expression data. Note that failing the permutation test may be an indication of lack of power to show that the expression significantly refines the direct SNP-trait signal. In practice, the permutation test was run 1,000 times for each TWAS gene and a p-value computed by Z-test against this null.
