Estimating heritability of complex traits from genome-wide association studies using IBS-based Haseman-Elston regression

Abstract

Exploring heritability of complex traits is a central focus of statistical genetics. Among various previously proposed methods to estimate heritability, variance component methods are advantageous when estimating heritability using markers. Due to the high-dimensional nature of data obtained from genome-wide association studies (GWAS) in which genetic architecture is often unknown, the most appropriate heritability estimator model is often unclear. The Haseman-Elston (HE) regression is a variance component method that was initially only proposed for linkage studies. However, this study presents a theoretical basis for a modified HE that models linkage disequilibrium for a quantitative trait, and consequently can be used for GWAS. After replacing identical by descent (IBD) scores with identity by state (IBS) scores, we applied the IBS-based HE regression to single-marker association studies (scenario I) and estimated the variance component using multiple markers (scenario II). In scenario II, we discuss the circumstances in which the HE regression and the mixed linear model are equivalent; the disparity between these two methods is observed when a covariance component exists for the additive variance. When we extended the IBS-based HE regression to case-control studies in a subsequent simulation study, we found that it provided a nearly unbiased estimate of heritability, more precise than that estimated via the mixed linear model. Thus, for the case-control scenario, the HE regression is preferable. GEnetic Analysis Repository (GEAR; http://sourceforge.net/p/gbchen/wiki/GEAR/) software implemented the HE regression method and is freely available.

Keywords: GWAS; Haseman–Elston regression; REML; case-control; identity by state; missing heritability; mixed linear model; variance component.

Figure 1

Estimation of heritability on the liability scale using the HE regression and mixed linear model methods. In each row, from left to right, each panel represents the case-control sample simulated under the same heritability on the liability scale (h²_l) but with different prevalence. In each panel, the vertical axis indicates the estimated heritability on the liability scale (h²_l), whereas the horizontal axis indicates which of the three methods (REML, non-constrained REML, and HE regression [least square estimate]) was used. The standard error of the mean (SEM) is indicated at the top of each bar.