randomly selected sets of control genes (with the latter matched to the former using the same effective number of SNPs per gene-set). Thus, a competitive test is of the null hypothesis is that these genes are not more strongly associated than a similar but randomly-selected set of genes. That is, the comparison is more one to the average degree of association across genes. The principal comparison is the competitive test, and we present self-contained tests for completeness. Competitive gene-set tests are more appropriate for a polygenic disease like schizophrenia because they explicitly prioritize gene-sets that show a greater average degree of association, over and above the polygenic background, rather than prioritizing larger but more weakly-enriched gene-sets (as self-contained tests would tend to do).
