To conduct the association analysis within UK Biobank we used BGENIE v1.1 51 to assess the effect of each genetic variant using a linear association test: y=Xβ+ε1 y^=Xβ (y−y^)=Gb+ε2 where y was the vector of binary observations for each phenotype (controls coded as 0 and cases coded as 1). β was the matrix of fixed effects, including sex, age, genotyping array, and the first 8 principal components and X was the corresponding incidence matrices. (y−y^) was a vector of phenotypes residualized on the fixed effect predictors, G was a vector of expected genotype counts of the effect allele (dosages), b was the effect of the genotype on residualized phenotypes, and ε1 and ε2 and were vectors of normally distributed errors. The effect sizes and standard errors were transformed to the logistic scale by dividing each value by ρ(1-ρ), where ρ is the trait prevalence (0.353).
