Integrating predicted transcriptome from multiple tissues improves association detection
Panel a illustrates the MultiXcan method. Predicted expression from all available tissue models are used as explanatory variables. To avoid multicolinearity, we use the first k Principal Components of the predicted expression. y is a vector of phenotypes for n individuals, is the standardized predicted gene expression for tissue j, gj is its effect size, a is an intercept and e is an error term. Panel b shows a schematic representation of MultiXcan results compared to classical PrediXcan, both for a single relevant tissue and all available tissues in agnostic scanning. y is a (centered) vector of phenotypes for n individuals, tj is the standardized predicted gene expression for model j, gj is its effect size in the joint regression, γj is its effect size in the marginal regression using only prediction j, e and ϵj are error terms.