Table 1 presents the simulation results when the multivariate phenotypes come from a multivariate normal distribution with the value of the correlation ϱ varied from 0 to 0.75. The numbers in each cell are the mean (standard deviation) of the indicator variable for p-value <0.05 among the 10,000 replications. The top panel corresponds to the case of β=(0,0,0,0,0)′ (i.e. when the null hypothesis is true) and thus can be used to evaluate if each of the competing methods was able to control the type I error. The results indicate that GEE and the Fisher combination test with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi _{2m}^{2}$\end{document}χ2m2 did not control the type I error rate when ϱ>0 while all the other methods did quite well under all values of ϱ. We, thus, did not find it meaningful to further compare these two methods with the other methods in terms of the statistical power. Table 1Simulation results when the multivariate phenotypes come from a multivariate normal distribution ϱ MANOVAPCAGEETATESFC-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\chi _{2m}^{2}$\end{document}χ2m2 FC-PermutationFC-PearsonFC-Kendall
