  The development of a complex disease is an intricate interplay of genetic and
environmental factors. "Heritability" is defined as the proportion of total
trait variance due to genetic factors within a given population. Studies with
monozygotic (MZ) and dizygotic (DZ) twins allow us to estimate heritability by
fitting an "ACE" model which estimates the proportion of trait variance
explained by additive genetic (A), common shared environment (C), and unique
non-shared environmental (E) latent effects, thus helping us better understand
disease risk and etiology. In this paper, we develop a flexible generalized
estimating equations framework ("GEE2") for fitting twin ACE models that
requires minimal distributional assumptions, rather only the first two moments
need to be correctly specified. We prove that two commonly used methods for
estimating heritability, the normal ACE model ("NACE") and Falconer's method,
can both be fit within this unified GEE2 framework, which additionally provides
robust standard errors. Although the traditional Falconer's method cannot
directly adjust for covariates, we show that the corresponding GEE2 version
("GEE2-Falconer") can incorporate covariate effects for both mean and
variance-level parameters (e.g. let heritability vary by sex or age). Given
non-normal data, we show that the GEE2 models attain significantly better
coverage of the true heritability compared to the traditional NACE and
Falconer's methods. Finally, we demonstrate an important scenario where the
NACE model produces biased estimates of heritability while Falconer's method
remains unbiased. Overall, we recommend using the robust and flexible
GEE2-Falconer model for estimating heritability in twin studies.
