## A Robust and Unified Framework for Estimating Heritability in Twin Studies using Generalized Estimating Equations

### Saonli Basu (September 19, 2018)

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### Abstract

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 and dizygotic 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. IIn 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 show 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, the corresponding GEE2 version (GEE2-Falconer'') can incorporate covarimate effects (e.g. let heritability vary by sex or age). Given non-normal data, these GEE2 models attain significantly better coverage of the true heritability compared to the traditional NACE and Falconer's methods. Finally, we demonstrate that Falconer's method can consistently estimate heritability when the ACE variance parameters differ between MZ and DZ twins; whereas the NACE will produce biased estimates in such settings.

Joint work with Jaron Arbet, Department of Biostatistics, University of Minnesota