Multiple correlated phenotypes are frequently collected in genome-wide association studies (GWASs), and a systematic, simultaneous analysis of multiple phenotypes can integrate the signals from single phenotypes, therefore increasing the power of detecting genetic signals. However, fundamental questions remain open, including the conditions and reasons under which the multivariate analysis is beneficial, how a highly significant signal arises in the multivariate analysis. To understand these issues, we propose to decompose the multivariate model into a series of simple univariate models. This transformation offers a clearer quantitative analysis of the circumstances under which a multivariate approach can be beneficial for the bivariate phenotypes case. A real data analysis is employed to illustrate how to interpret how the signals arising from multivariate GWASs.
Keywords: GWAS; multivariate analysis; univariate decomposition.
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