“…The most widely used strategies for those research efforts are combining univariate analysis results, dimension reduction, and regression models. Methods involving the first strategy combine either the univariate test statistics (Kim, Bai, & Pan, 2015;O'Brien, 1984;Wei & Johnson, 1985) or p-values (Liang, Wang, Sha, & Zhang, 2016;van der Sluis, Posthuma, & Dolan, 2013;Yang, Li, Williams, & Buu, 2016); they are generally very easy to implement and can cope with a mixture of different types of phenotypes; however, the statistical power of those methods might heavily rely on the homogeneity of univariate test statistics (Zhu, Zhang, & Sha, 2015;Zhu, Zhang, & Sha, 2018); the most popular methods in this category include O'Brien's method (O'Brien, 1984;Wei & Johnson, 1985), trait-based association test that uses extended Simes procedure (TATES; van der Sluis et al, 2013), Fisher's combination (Yang et al, 2016), and adaptive Fisher's combination (AFC; Liang et al, 2016). For the strategy of dimension reduction, instead of testing one phenotype at a time, one first constructs a small number of latent variables, which are linear combinations of the observed phenotypes, and then tests the associations between the latent variables and the genetic variant of interest; dimension reduction methods are, in general, suitable only when all phenotypes are normally distributed (Yang & Wang, 2012); in addition, the newly derived latent variables are usually difficult to interpret in the real-world applications; the most popular methods in this category include principal components of the phenotypes (Aschard et al, 2014), principal component of heritability (Klei, Luca, Devlin, & Roeder, 2008;Zhou et al, 2015), and canonical correlation analysis (Ferreira & Purcell, 2008;Tang & Ferreira, 2012).…”