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Chunk #53 — Method — Standardization and Scaling of Summary Statistics for Multivariate GWAS

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Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits.
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When OLS regression coefficients and standard errors are provided from an analysis in which the phenotype has not been standardized prior to analyses, or only Z statistics or p-values (for which Z statistics can be readily obtained) are provided, the partially standardized regression coefficients and their standard errors can be obtained as Z=bSNP,P∗SEbSNP,P∗, bSNP,P=ZNσSNP2, and SEbSNP,P=bSNP,PZ, where bSNP,P∗ is equal to the regression coefficient for the OLS GWAS of the unstandardized phenotype. These derived partially standardized coefficients are then transformed into covariances by multiplying by the variance of scores on the SNP, as per above.