In GWAS for complex diseases, the association between a SNP and each phenotype is usually weak. Combining multiple related phenotypic traits can increase the power of gene search and thus is a practically important area that requires methodology work. This study provides a comprehensive review of existing methods for conducting GWAS on complex diseases with multiple phenotypes including MANOVA, PCA, GEE, TATES, and the classical Fisher combination test. Built upon the Fisher combination test, we proposed a new method that relaxes the unrealistic independence assumption and is also computationally efficient. Particularly, in an exploratory study where multiple sets of phenotypes may be of interest, when the set is changed, our proposed methods only require re-calculation of the correlation between phenotypes and then the available marginal p-values for each SNP can be re-used. The competing methods which do not involve marginal p-values such as the PCA, MANOVA, and GEE, on the other hand, would require a complete re-analysis.
