Table 3.

Summary of the number of SNP pairs detected by different filtering methods.

Univariate			Bivariate Filter				Bivariate Filter + GSS
Dataset	log10 $P_{{\chi }^2}$		${\chi }^2$		DSS	GBOOST		${\chi }^2$	DSS	GBOOST
HT	-9.8		128		429	51		41	107	24
BD	-10.9		2445		556	34		44	179	27
CAD	-13.1		210147		7807	43		42	116	39
T2D	-13.3		56592		3105	52		79	134	41
CD	-34.3		> 500000∗		5591	25		29	57	22
RA	-37.7		> 500000∗		823	99		59	312	95
T1D	-133.6		> 500000∗		4993	37		2	107	33

Summary of the number of SNP pairs detected by ${\chi }^2$, GBOOST and our introduced DSS heuristic over all WTCCC datasets before and after filtering with GSS. The rows of the table are sorted in descending order of p-values for univariate ${\chi }^2$ test (Column 2). Columns 3-5 show results for the bivariate filters, and columns 6-8 show the number of epistatic interactions discovered after further filtering with GSS. In some diseases, strong univariate SNPs likely cause proliferation of non-epistatic but significant pairs according to ${\chi }^2$. These pairs are largely removed by the proposed GSS filter. A '*' indicates that an upper bound on the number of recorded pairs was reached. The number of significant pairs may be much higher.