Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Abstract

Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of geneenvironment (G 3 E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G 3 E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of .10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to $50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G 3 E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.KEYWORDS twin models; penalized B-splines; age-specific heritability; empirical Bayes predictor; body mass index T WIN studies have been broadly used as a tool to investigate heritability for decades. A recent comprehensive meta-analysis reported 17,804 heritability estimates for various traits based on twin studies (Polderman et al. 2015).Estimation methods and software such as structural equation modeling (SEM) based on the classical twin models consisting of additive genetic, common, and unshared environmental effects have been well established and extensively adopted (Rijsdijk and Sham 2002). Extensions for longitudinal data or time-to-event phenotypes based on the classical twin models have been proposed (Boomsma et al. 1989;Pitkäniemi et al. 2007). Nevertheless, one of...

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