Bayesian inference analyses of the polygenic architecture of rheumatoid arthritis

Abstract

The genetic architectures of common, complex diseases are largely uncharacterized. We modeled the genetic architecture underlying genome-wide association study (GWAS) data for rheumatoid arthritis and developed a new method using polygenic risk-score analyses to infer the total liability-scale variance explained by associated GWAS SNPs. Using this method, we estimated that, together, thousands of SNPs from rheumatoid arthritis GWAS explain an additional 20% of disease risk (excluding known associated loci). We further tested this method on datasets for three additional diseases and obtained comparable estimates for celiac disease (43% excluding the major histocompatibility complex), myocardial infarction and coronary artery disease (48%) and type 2 diabetes (49%). Our results are consistent with simulated genetic models in which hundreds of associated loci harbor common causal variants and a smaller number of loci harbor multiple rare causal variants. These analyses suggest that GWAS will continue to be highly productive for the discovery of additional susceptibility loci for common diseases.

Figure 1

Association of polygenic risk scores with common disease case-control status in independent validation datasets. Association P values (log₁₀ scale) are plotted, with the number of SNPs used for the calculation of the risk scores shown at right, for SNP sets based on P_GWAS thresholds ranging from 10⁻⁴ (top, green) to 0.5 (bottom, blue). (a) Rheumatoid arthritis (all known risk loci removed). (b) Celiac disease (with the extended MHC region removed). (c) Myocardial infarction (discovery data) and coronary artery disease (test data). (d) T2D.

Figure 2

Posterior probability densities of the number of associated SNPs and the total liability-scale variance explained for the Bayesian analysis of the polygenic analysis results. N_SNPs are shown on the log₁₀ scale on the x axis, and V_tot values are shown on the y axis. The heat map colors represent the probability density height, with darker colors indicating higher density. Contour lines show the highest posterior density and the 50%, 90% and 95% credible regions. (a) Rheumatoid arthritis (with all known risk loci removed). (b) Celiac disease (with the extended MHC region removed). (c) MI/CAD. (d) T2D.

Figure 3

Posterior probability distributions of the relative risk and minor allele frequency of the inferred disease-associated SNPs. The GRR is shown on the y axis in the left and middle images, and the MAF is shown on the x axis in the middle and bottom images. Heat map colors indicate the mean posterior numbers of SNPs in risk allele frequency (RAF)-GRR bins scaled to the posterior mean number of disease-associated SNPs (indicated in the legend). The graphs on the left and at the bottom show the marginal posterior (solid line) and prior (dashed line) probability densities. (a) Rheumatoid arthritis (with all known risk loci removed). (b) Celiac disease (with the extended MHC region removed). (c) MI/CAD. (d) T2D.

Figure 4

Causal variants underlying the rheumatoid arthritis polygenic disease architecture inferred from the GWAS data. Plotted are the liability-scale variances explained (V_tot, bars, left y axes) and the number of loci harboring causal variants (black line, right y axes). The colored sections in the bars partition the V_tot values for previously validated common SNP associations (gray), undiscovered GWAS SNP associations induced by causal variants (blue) and causal variants (V_tot, in addition to the values for GWAS SNPs, red). Error bars show 95% confidence intervals for causal variant numbers and V_tot values based on simulations achieving a GWAS SNP V_tot value equal to that inferred from the polygenic modeling. Six plausible causal variant models are plotted (left to right): (i) 1,900 loci each with a single common (MAF > 5%) causal variant, (ii) 894 loci each with 2 common causal variants, (iii) 391 loci each with 4 common causal variants, (iv) 155 loci each with 8 rare (MAF < 1%) causal variants, (v) 16 rare causal variants per locus with v = 0.0005 and (vi) a mixture (60:40 ratio of model 2 to model 4 in terms of GWAS SNPs V_tot values, implying 536 common causal variant loci and 62 rare causal variant loci). The per-causal–variant liability-scale variances explained (v) for models that are consistent with the polygenic modeling and inference results were v = 0.0001 for common causal variants and v = 0.0005 for rare causal variants.