We conducted a simulation study to compare the performance of the competing methods. The GEE and the Fisher combination test with the independence assumption did not control the type I error rate and thus are not recommended. In general, the power of the methods decreased as the correlation between phenotypes increased. Furthermore, all the competing methods tended to have lower power when the multivariate phenotypes come from long tailed distributions. The proposed method (with the correlation being estimated by the Pearson’s sample correlation coefficient or the Kendall’s τ) performed as well as the permutation method and yet only required 10−2 computational time. In most settings of the simulation, these three Fisher combination tests outperformed the other methods. The real data analysis also demonstrated that the Fisher combination tests allow us to compare the marginal results with the multivariate results and specify which SNPs are specific to a particular phenotype or contribute to the common construct.
