Efficient Multiple-Trait Association and Estimation of Genetic Correlation Using the Matrix-Variate Linear Mixed Model

Abstract

Multiple-trait association mapping, in which multiple traits are used simultaneously in the identification of genetic variants affecting those traits, has recently attracted interest. One class of approaches for this problem builds on classical variance component methodology, utilizing a multitrait version of a linear mixed model. These approaches both increase power and provide insights into the genetic architecture of multiple traits. In particular, it is possible to estimate the genetic correlation, which is a measure of the portion of the total correlation between traits that is due to additive genetic effects. Unfortunately, the practical utility of these methods is limited since they are computationally intractable for large sample sizes. In this article, we introduce a reformulation of the multiple-trait association mapping approach by defining the matrix-variate linear mixed model. Our approach reduces the computational time necessary to perform maximum-likelihood inference in a multiple-trait model by utilizing a data transformation. By utilizing a well-studied human cohort, we show that our approach provides more than a 10-fold speedup, making multiple-trait association feasible in a large population cohort on the genome-wide scale. We take advantage of the efficiency of our approach to analyze gene expression data. By decomposing gene coexpression into a genetic and environmental component, we show that our method provides fundamental insights into the nature of coexpressed genes. An implementation of this method is available at http://genetics.cs.ucla.edu/mvLMM. KEYWORDS association studies; multivariate analysis; genetic correlation C LASSICALLY, genome-wide association studies have been carried out using single traits. However, it is well known that genes often affect multiple traits, a phenomenon known as pleiotropy, and more recently it has been shown that performing association mapping with multiple traits simultaneously may increase statistical power (Korol et al. 2001;Ferreira and Purcell 2009;Liu et al. 2009;Avery et al. 2011;Korte et al. 2012). Analysis of multiple traits increases power because intuitively, multiple-trait measurements increase sample size relative to a single-trait measurement. However, utilizing the additional data is not straightforward as measurements from the same individual are not independent. This issue is analogous to that of association analysis in cohorts of related individuals, where trait measurements between related individuals are not independent. Variance component methods model this correlation structure by assuming that the covariance due to genetics between related individuals is proportional to their kinship coefficient (Kang et al. 2008). This constant of proportionality normalized by the total trait variance is related to narrow-sense heritability of the trait (the variance accounted for by additive genetic effects) .When the same genetic variants affect multiple traits, trait values for an individual will tend to be correlated. Similarly, shar...

Do Molecular Markers Inform About Pleiotropy?

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Literature Reviews on Methods for Rare Variant Association Studies

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GW-SEM: A Statistical Package to Conduct Genome-Wide Structural Equation Modeling

“…On a server with parallel processing capacity, analysis time could be substantially reduced to a few hours. While this length of time is reasonable, it is inevitably slower than other MV-GWAS methods that treat the items as continuous variables (Zhou & Stephens, 2014, 2012; Furlotte & Eskin, 2015; Meyer & Tier, 2012). …”

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