Abstract
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.