Last updated: 2022-11-09

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Introduction to MESuSiE

MESuSiE is a multiple ancestry extension of Sum of Single Effect model for GWAS fine-mapping. MESuSiE assumes that the causal SNPs are shared across ancestries, thought differ in effect size due to allele heterogeneity, and hence the power of analysis increases by jointly modelling the effect across ancestries. By leveraging the independent effect assumption of SuSie, MESuSiE models the correlation structure of the effect sizes of causal SNPs across ancestries, and therefore further improve the power of causal SNP detection.

MESuSiE Overview

MESuSiE relies on GWAS summary statistics from multiple ancestries, properly accounts for the LD structure of the focal genomic region in multiple ancestries, and explicitly models both shared and ancestry-specific causal signals to accommodate causal effect size similarity as well as heterogeneity across ancestries. MESuSiE outputs posterior inclusion probability of variant being shared or ancestry-specific causal variants.

MESuSiE Model

MESuSiE builds upon the sum of single effect model, and extend the normal assumption on the effec size of causal SNP to multivariate normal, and thus capture the correlation across ancestries. fashion: \[ \left(\begin{matrix}{y}_\mathbf{1}\\{y}_\mathbf{2}\\\end{matrix}\right)=\left[\begin{matrix}{X}_\mathbf{1}&0\\0&{X}_\mathbf{2}\\\end{matrix}\right]\ast\left(\begin{matrix}{b}_\mathbf{1}\\{b}_\mathbf{2}\\\end{matrix}\right)+\left(\begin{matrix}{\epsilon}_\mathbf{1}\\{\epsilon}_\mathbf{2}\\\end{matrix}\right), \] In the above equation, \(y_1,y_2\) are standardized phenotype for each ancestry, \(X_1,X_2\) are centered genotype matrices, \(b_1,b_2\) are sum of the single effect models which are in the form, \[ \left(\begin{matrix}{b}_\mathbf{1}\\{b}_\mathbf{2}\\\end{matrix}\right) = \sum_l \gamma_l\bigotimes \left(z_l\cdot\left(\begin{matrix}{\beta}_\mathbf{1l}\\{\beta}_\mathbf{2l}\\\end{matrix}\right) \right) \] which represents the summation of the single effects.