The Annals of Applied Statistics

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

Armin Schwartzman, Andrew J. Schork, Rong Zablocki, and Wesley K. Thompson

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Analysis of genome-wide association studies (GWAS) is characterized by a large number of univariate regressions where a quantitative trait is regressed on hundreds of thousands to millions of single-nucleotide polymorphism (SNP) allele counts, one at a time. This article proposes an estimator of the SNP heritability of the trait, defined here as the fraction of the variance of the trait explained by the SNPs in the study. The proposed GWAS heritability (GWASH) estimator is easy to compute, highly interpretable and is consistent as the number of SNPs 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, we establish the theoretical properties of the GWASH estimator and obtain analytical estimates of the precision, allowing for power and sample size calculations for SNP heritability estimates and forming a firm foundation for future methodological development.

Article information

Ann. Appl. Stat., Volume 13, Number 4 (2019), 2509-2538.

Received: December 2017
Revised: April 2019
First available in Project Euclid: 28 November 2019

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High dimensional data massively univariate regression summary statistics single nucleotide polymorphism


Schwartzman, Armin; Schork, Andrew J.; Zablocki, Rong; Thompson, Wesley K. A simple, consistent estimator of SNP heritability from genome-wide association studies. Ann. Appl. Stat. 13 (2019), no. 4, 2509--2538. doi:10.1214/19-AOAS1291.

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Supplemental materials

  • A simple, consistent estimator of SNP heritability from genome-wide association studies. Derivations, proofs and efficient computations.
  • Software. R code implementing the GWASH estimator and the numerical simulations above may be found in