  Genome-wide association studies (GWAS) have identified thousands of genetic
variants associated with complex traits, and some variants are shown to be
associated with multiple complex traits. Genetic covariance between two traits
is defined as the underlying covariance of genetic effects and can be used to
measure the shared genetic architecture. The data used to estimate such a
genetic covariance can be from the same group or different groups of
individuals, and the traits can be of different types or collected based on
different study designs. This paper proposes a unified regression-based
approach to robust estimation and inference for genetic covariance of general
traits that may be associated with genetic variants nonlinearly. The asymptotic
properties of the proposed estimator are provided and are shown to be robust
under certain model mis-specification. Our method under linear working models
provides a robust inference for the narrow-sense genetic covariance, even when
both linear models are mis-specified. Numerical experiments are performed to
support the theoretical results. Our method is applied to an outbred mice GWAS
data set to study the overlapping genetic effects between the behavioral and
physiological phenotypes. The real data results reveal interesting genetic
covariance among different mice developmental traits.
