We applied causal mixture models49,118 to the GWAS summary statistics, using MiXeR v1.3. MiXeR provides univariate estimates of the proportion of non-null SNPs (“polygenicity”) and the variance of effect sizes of non-null SNPs (“discoverability”) in each phenotype. For each SNP, i, univariate MiXeR models its additive genetic effect of allele substitution, βi, as a point-normal mixture, βi=(1−π1)N(0,0)+π1N(0, σβ2), where π1 represents the proportion of non-null SNPs (`polygenicity`) and σβ2 represents variance of effect sizes of non-null SNPs (`discoverability`). Then, for each SNP, j, MiXeR incorporates LD information and allele frequencies for M = 9,997,231 SNPs extracted from 1000 Genomes Phase 3 data to estimate the expected probability distribution of the signed test statistic, zj=δj+ϵj=N∑iHirijβi+ϵj, where N is sample size, Hi indicates heterozygosity of i-th SNP, rij indicates allelic correlation between i-th and j-th SNPs, and ϵj~N(0, σ02) is the residual variance. Further, the three parameters, π1, σβ2, σ02, are fitted by direct maximization of the likelihood function. The optimization is based on a set of approximately 600,000 SNPs, obtained by selecting a random set of 2,000,000 SNPs with minor allele
