as competitive and self-contained tests, respectively. While a competitive test compares disease association test statistics for genes in the gene set versus that for genes in the rest of the genome, a self-contained test directly tests gene set association with disease and does not depend on genes outside the gene set. Table 1 lists some examples of competitive tests for gene set analysis of GWAS, including GSEA, over-representation analysis based on Fisher’s exact test (hypergeometric test) and their extensions such as ALIGATOR [31] and GSA-SNP [32]. Table 2 lists some examples of self-contained tests, including the SNP Ratio Test [6], GRASSS [33] and the SPCA method [12]. When the “real” causal SNPs are fully contained in one particular gene set, testing Q1 and Q2 are approximately the same. However, when SNPs in multiple gene sets are associated with the disease or when causal genes are shared by multiple gene sets, using competitive tests that compare gene set association signals with the rest of the genome may result in loss of power [8,34]. For example, Tintle et al. [35] found the SUMSTAT statistics (based on the MAX-MIN statistic [36]) performed better than GSEA and Fisher’s exact test.
