A new method for estimating effect size distribution and heritability from genome-wide association summary results

Accurately estimating the distribution and heritability of SNP effects across the genome could help explain the mystery of missing heritability. In this study, we propose a novel statistical method for estimating the distribution and heritability of SNP effects from genome-wide association studies (GWASs), and compare its performance to several existing methods using both simulations and real data. Specifically, we study the full range of GWAS summary results and link observed p values and unobserved effect sizes by (non-central) Chi-square distribution. By modeling the observed full set of association signals using a multinomial distribution, we build a likelihood function of SNP effect sizes using parametric and non-parametric maximum likelihood frameworks. Simulation studies show that the proposed method can accurately estimate effect sizes and the number of associated SNPs. As real applications, we analyze publicly available GWAS summary results for height, body mass index (BMI), and bone mineral density (BMD). Our analyses show that there are over 10,000 SNPs that might be associated with height, and the total heritability attributable to these SNPs exceeds 70 %. The heritabilities for BMI and BMD are ~10 and ~15 %, respectively. The results indicate that the proposed method has the potential to improve the accuracy of estimates of heritability and effect size for common SNPs in large-scale GWAS meta-analyses. These improved estimates may contribute to an enhanced understanding of the genetic basis of complex traits.