Joint Regression Analysis of Multiple Traits Based on Genetic Relationships

Abstract

Polygenic scores (PGSs) are widely available and employed in genomic data analyses for predicting and understanding genetic architectures. We propose a novel clustering and estimation method using PGSs for inferring a genetic relationship among multiple, simultaneously measured and potentially correlated traits in a multivariate GWAS. Using graphical lasso, we estimate a sparse covariance matrix of the PGSs and obtain clusters of traits sharing genetic characteristics. We use the clusters to specify the structure of the error covariance matrix of a generalised least squares (GLS) model and use the feasible GLS estimator for estimating a linear regression model with a certain unknown degree of correlation between the residuals. The method suits many biology studies well with traits embedded in some genetic functioning groups and facilitates developement of the PGS research. We compare the method with fully parametric techniques on simulated data and illustrate the utility of the methods by examining a heterogeneous stock mouse data set from the Wellcome Trust Centre for Human Genetics. We demonstrate that the method successfully identifies clusters of traits and increases precision, power and computational efficiency.