A robust and unified framework for estimating heritability in twin studies using generalized estimating equations

Abstract

The ‘heritability’ of a phenotype measures the proportion of trait variance due to genetic factors in a population. In the past 50 years, studies with monozygotic and dizygotic twins have estimated heritability for 17,804 traits;1 thus twin studies are popular for estimating heritability. Researchers are often interested in estimating heritability for non‐normally distributed outcomes such as binary, counts, skewed or heavy‐tailed continuous traits. In these settings, the traditional normal ACE model (NACE) and Falconer's method can produce poor coverage of the true heritability. Therefore, we propose a robust generalized estimating equations (GEE2) framework for estimating the heritability of non‐normally distributed outcomes. The traditional NACE and Falconer's method are derived within this unified GEE2 framework, which additionally provides robust standard errors. Although the traditional Falconer's method cannot adjust for covariates, the corresponding ‘GEE2‐Falconer’ can incorporate mean and variance‐level covariate effects (e.g. let heritability vary by sex or age). Given a non‐normally distributed outcome, the GEE2 models are shown to attain better coverage of the true heritability compared to traditional methods. Finally, a scenario is demonstrated where NACE produces biased estimates of heritability while Falconer remains unbiased. Therefore, we recommend GEE2‐Falconer for estimating the heritability of non‐normally distributed outcomes in twin studies.

Heritability estimation of cognitive phenotypes in the ABCD Study®using mixed models

“…The last several years have seen the development of several new techniques that can be used to model additional relationships, such as random effect × time interaction (He et al 2016), random effect × covariate interaction (Arbet et al 2020), covariance among random effects (Zhou et al 2020; Dolan et al 2021), and allowing random effects estimates to vary as a function of the phenotype (Azzolini et al 2022). The sparse clustering design employed in the FEMA package leads to improved computational efficiency compared to other LME implementation software (Fan et al 2021); future work will investigate the use of FEMA to estimate random effects estimates in more high-dimensional datasets, such as the brain imaging data present in the ABCD Study ® , and compare with other computationally efficient implementations of the ACE Model such as Accelerated Permutation Inference for the ACE Model (APACE; Chen et al 2019) and positive semidefinite ACE (PSD-ACE; Risk and Zhu 2021).…”

Estimating heritability of height without zygosity information for twins under five years in low- and middle-income countries: An application of normal finite mixture distribution models

“…We describe the approach here for a generic outcome y . Following ( Arbet et al, 2020 ), we suppose that where variance components (additive genetic), (common shared family environment), and (nonshared environmental) are random effects drawn from distributions that depend on the zygosity of the twin, z . The key assumption has to do with the distributions underlying these random effects.…”

Gene-environment interactions explain a substantial portion of variability of common neuropsychiatric disorders

“…With the strong assumption that the environment is identical for both individuals in each twin pair, we can then use a simple model to attribute disease status in concordance to the twins' genetic similarity. [7][8][9][10][11] Pedigree studies These limited phenotypic data include disease or no-disease statuses for each family member. Genetic data are reduced to a pedigree structure, in which siblings share half of the genetic variants with each parent and with each other.…”

“…With the strong assumption that the environment is identical for both individuals in each twin pair, we can then use a simple model to attribute disease status in concordance to the twins’ genetic similarity. 7 , 8 , 9 , 10 , 11 …”