Estimation of genetic correlation with summary association statistics

Summary Genome-wide association studies have identified thousands of genetic variants that are associated with complex traits. Many complex traits are shown to share genetic etiology. Although various genetic correlation measures and their estimators have been developed, rigorous statistical analysis of their properties, including their robustness to model assumptions, is still lacking. We develop a method of moments estimator of genetic correlation between two traits in the framework of high-dimensional linear models. We show that the genetic correlation defined based on the regression coefficients and the linkage disequilibrium matrix can be decomposed into both the pleiotropic effects and correlations due to linkage disequilibrium between the causal loci of the two traits. The proposed estimator can be computed from summary association statistics when the raw genotype data are not available. Theoretical properties of the estimator in terms of consistency and asymptotic normality are provided. The proposed estimator is closely related to the estimator from the linkage disequilibrium score regression. However, our analysis reveals that the linkage disequilibrium score regression method does not make full use of the linkage disequilibrium information, and its jackknife variance estimate can be biased when the model assumptions are violated. Simulations and real data analysis results show that the proposed estimator is more robust and has better interpretability than the linkage disequilibrium score regression method under different genetic architectures.