A Unified Approach to Robust Inference for Genetic Covariance

Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex traits. Many complex traits are found to have shared genetic etiology. Genetic covariance is defined as the underlying covariance of genetic values and can be used to measure the shared genetic architecture. The data of two outcomes may be collected from the same group or different groups of individuals and the outcomes can be of different types or collected based on different study designs. This paper proposes a unified approach to robust estimation and inference for genetic covariance of general outcomes that may be associated with genetic variants nonlinearly. We provide the asymptotic properties of the proposed estimator and show that our proposal is robust under certain model mis-specification. Our method under linear working models provides robust inference for the narrow-sense genetic covariance, even when both linear models are mis-specified. Various 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 demonstrate the robustness of the proposed method and reveal interesting genetic covariance among different mice developmental traits.