A simple, consistent estimator of heritability for genome-wide association studies

Abstract

Analysis of genome-wide association studies (GWAS) is characterized by a large number of univariate regressions where an outcome, a quantitative trait, is regressed on hundreds of thousands to millions of genomic markers, i.e. single-nucleotide polymorphism (SNP) counts, one marker at a time. Assuming a linear model linking the markers to the outcome, this article proposes an estimator of the heritability of the trait, defined here as the fraction of the variance of the trait explained by the genomic markers in the study. The estimator, called GWAS heritability (GWASH) estimator, is easy to compute, highly interpretable, and is consistent as the number of markers and the sample size increase. More importantly, it can be computed from summary statistics typically reported in GWAS, not requiring access to the original data. The estimator takes full account of the linkage disequilibrium (LD) or correlation between the SNPs in the study through moments of the LD matrix, estimable from auxiliary datasets. Unlike other proposed estimators in the literature, the precision of the estimate is obtainable analytically, allowing for power and sample size calculations for heritability estimates.