Table 7.

Likelihood of Observed Gene Sharing between Selected Pairs of Different Traits and a Comparison of Three Modeling Approaches for Selected Trait Pairs

Trait	Number of Genes Associated to Trait	Other Trait	Number of Genes Associated to Other Trait	Number of Genes Shared between Traits	p Values
					Independent Model		Degree of Surprise, Accounting for Dissimilaritiesa
					Estimated Total Number of Genes, n = 20,000	Genes Present in the NHGRI Catalog, n = 1380
Schizophrenia	16	iron markers	7	2	1.60 × 10−5	0.003	0.76
Schizophrenia	16	uric acid and gout	16	2	8.10 × 10−5	0.0143	0.85
Cancer-related traits	154	PSA	6	4	1.80 × 10−7	0.0043	0.98
Cancer-related traits	154	pigmentation traits	19	5	4.90 × 10−7	0.0428	0.98
Cancer-related traits	154	immune traits	265	19	1.00 × 10−12	0.0101	1
Infections	29	immune traits	265	5	5.10 × 10−5	0.1706	0.99
SLE	26	corpuscular volume	29	3	8.70 × 10−6	0.0157	0.94

^aCriterion is corrected for the noise in the data, namely the possibility of false positives and false negatives (see Supplemental Data for details). To ensure a fair comparison between the DS approach and the independent model, we assumed that the probabilities of genetic matches $p_i$ were identical for all genes in the GWAS corpus; we also replaced the random sampling of pairs of diseases and/or traits by an exhaustive averaging over all $n_g\left(n_g+1\right)/2$ combinations.