These gene-sets were tested for association with the GWGAS gene-based test statistics using MAGMA. We computed competitive P-values, which represent the test of association for a specific gene-set compared to other gene-sets. This method is more robust to Type I error than self-contained tests that only test for association of a gene-set against the null hypothesis of no association25. The Bonferroni-corrected significance threshold was 0.05/7,323 gene-sets=6.83×10-6. Conditional analyses were performed as a follow-up using MAGMA to test whether each significant association observed was independent of all others. The association between each gene-set was tested conditional on the most strongly associated set, and then - if any substantial (p<.05/number of gene-sets) associations remained - by conditioning on the first and second most strongly associated set, and so on until no associations remained. Gene-sets that retained their association after correcting for other sets were considered to be independent signals. We note that this is not a test of association per se, but rather a strategy to identify, among gene-sets with known significant associations whose defining genes may overlap, which set(s) are responsible for driving the observed association.
