Nick FurlotteMultiple trait association mapping, a procedure in which multiple traits are used simultaneously to identify genetic variants affecting those traits, has recently attracted interest. One class of approaches for this problem builds on classical variance component methodology, utilizing a multi-trait 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, or the proportion 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 paper, we introduce a reformulation of the multiple trait association mapping approach using a matrix-variate linear mixed-model, which allows us to perform association analysis in computational time linear in the size of the data, as opposed to current methods which are cubic in the size of the data. By utilizing a well-studied human cohort, we show that our approach provides more than a 150-fold speed up, making multiple phenotype association feasible in a large population cohort on the genome-wide scale. We take advantage of the efficiency of our approach to analyze expression quantitative trait loci (eQTLs), where genetic variants are tested for association with thousands of phenotypes. By decomposing gene coexpression into a genetic and environmental component, we show that our method provides fundamental insights into the nature of co-expressed genes.
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