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.

Keywords: generalized estimating equations; heritability; twin studies.

FIGURE 1

NACE is biased given unequal MZ and DZ variance while Falconer’s method remains unbiased

FIGURE 2

Histograms of 5 substance-abuse traits from the Minnesota Center for Twin and Family Research study. For each trait, there were 936 MZ and 478 DZ twin pairs. Nicotine (NIC): composite measure of nicotine use and dependence; Alcohol Consumption (CON): composite of measures of alcohol use frequency and quantity; Illicit Drugs (DRG): composite of frequency of use of 11 different drug classes and DSM symptoms of drug dependence; Behavioral Disinhibition (BD): composite of measures non-substance use behavioral disinhibition including symptoms of conduct disorder and aggression; Externalizing Factor (EXT): a composite measure of all five previous traits

FIGURE 3

GEE2-Falconer model with h², c², e² allowed to vary as a non-linear function of Age (with 95% confidence intervals) for a longitudinal alcohol use trait from the Minnesota Center for Twin and Family Research study. There were 611 MZ and 341 DZ twin pairs with the outcome measured at all ages 17, 20, 24, and 29. h², c², e²: proportion of total trait variance due to additive genetic effects, common shared environmental effects, and unique non-shared environmental effects respectively