Beyond SNP heritability: Polygenicity and discoverability of phenotypes estimated with a univariate Gaussian mixture model.

QQ plots of (pruned) z-scores for qualitative phenotypes (dark blue, 95% confidence interval in light blue) with model prediction (yellow): (A) major depressive disorder; (B) bipolar disorder; (C) schizophrenia; (D) coronary artery disease (CAD); (E) ulcerative colitis (UC); (F) Crohn’s disease (CD); (G) late onset Alzheimer’s disease (AD), excluding APOE (see also S1 Appendix (p. S17)); and (H) amyotrophic lateral sclerosis (ALS), restricted to chromosome 9 (see also S1 Appendix (p. S18)).The dashed line is the expected QQ plot under null (no SNPs associated with the phenotype). p is a nominal p-value for z-scores, and q is the proportion of z-scores with p-values exceeding that threshold. λ is the overall nominal genomic control factor for the pruned data (which is accurately predicted by the model in all cases). The three estimated model parameters are: polygenicity, π^1; discoverability, σ^β2 (corrected for inflation); and SNP association χ2-statistic inflation factor, σ^02. h^2 is the estimated narrow-sense chip heritability, re-expressed as hl2 on the liability scale for these case-control conditions assuming a prevalence of: MDD 7.1% [57], BIP 0.5% [58], SCZ 1% [59], CAD 3% [60], UC 0.1% [61], CD 0.1% [61], AD 14% (for people aged 71 and older in the USA [62, 63]), and ALS 5 × 10−5 [64]. The estimated number of causal SNPs is given by n^causal=π^1nsnp where nsnp = 11, 015, 833 is the total number of SNPs, whose LD structure and MAF underlie the model; the GWAS z-scores are for subsets of these SNPs. Neff is the effective case-control sample size–see text. Reading the plots: on the vertical axis, choose a p-value threshold (more extreme values are further from the origin), then the horizontal axis gives the proportion of SNPs exceeding that threshold (higher proportions are closer to the origin). Numerical values for the model parameters are also given in Table 2. See also S1 Appendix (pp. S20-S28).

this area for notes QQ plots of (pruned) z-scores and model fits for quantitative phenotypes: (A) educational attainment; (B) intelligence; (C) body mass index (BMI); (D) height; (E) putamen volume; (F) low-density lipoprotein (LDL); (G) high-density lipoprotein (HDL); and (H) total cholesterol (TC).N is the sample size. See Fig 1 for further description. Numerical values for the model parameters are also given in Table 2. See also S1 Appendix (pp. S29-S38).

Proportion of narrow-sense chip heritability, A(N) (Eq 37), captured by genome-wide significant SNPs as a function of sample size, N, for phenotypes shown in Figs 1 and Fig 2.Values for current sample sizes are shown in parentheses. Left-to-right curve order is determined by decreasing σβ2. The prediction for education at sample size N = 1.1 million is A(N) = 0.27, so that the proportion of phenotypic variance explained is predicted to be 3.5%, in good agreement with 3.2% reported in [70]. (The curve for AD excludes the APOE locus. For HDL, see S1 Appendix (p. S9) for additional notes).