Linear mixed model for heritability estimation that explicitly addresses environmental variation

Abstract

The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://github.com/MicrosoftGenomics/FaST-LMM.

Keywords: Gaussian radial basis function; environment; heritability estimation; linear mixed model; model misspecification.

Fig. 1.

Uncorrected and corrected estimates of narrow-sense heritability for phenotypes from the Ugandan cohort. The height of the blue and red bar combined corresponds to the uncorrected heritability estimate (based on Eq. 3). The height of the blue bar corresponds to the corrected heritability estimate (based on Eq. 5). Asterisks denote differences that are statistically significant after Bonferroni correction based on a two-sided test on the difference between uncorrected and corrected estimates from a 500-group jackknife.