Extended Data Figure 7. Epistasis.

Quantile-quantile plot for all pair-wise (N=7750) combinations of the 125 independent autosomal genome-wide significant SNPs tested for non-additive effects on risk using case-control datasets of European ancestry (32,405 cases and 42,221 controls). We included as covariates the principal components from the main analysis as well as a study indicator. The interaction model is described by:

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3\ast {X_1}^{\ast }{X}_2+{\beta }_4{X}_4+{\beta }_5{X}_5$$

X₁ and X₂ are genotypes at the two loci, X₁*X₂ is the interaction between the two genotypes modeled in a multiplicative fashion, X₄ is the vector of principal components, X₅ is the vector of study indicator variables. Each β is the regression coefficient in the generalized linear model using logistic regression. The overall distribution of P-values did not deviate from the null and the smallest P-value (4.28×10⁻⁴) did not surpass the Bonferroni correction threshold (p=0.05/7750= 6.45×10⁻⁶). The line x=y indicates the expected null distribution with the grey area bounded by red lines indicating the expected 95% confidence interval for the null.