Finally, we performed a power comparison between the four-phenotype analysis and the two-phenotype analysis using GEMMA, using simulations based on the two data sets. Specifically, we used the same set of 10,000 SNPs described above to act as causal SNPs, and we simulated phenotypes by adding genotype effects to the observed phenotypes, as above. For each causal SNP, we made it to affect either one, two, three or four phenotypes. When the causal SNP affected two or four phenotypes, its effects on randomly selected half of the traits were in the opposite direction as its effects on the other half. When the causal SNP affected three phenotypes, its effects on randomly selected two traits were in the opposite direction as its effect on the third trait. The SNP effect size for each affected phenotype was simulated independently to account for a pre-specified PVE of that phenotype (ranged from 0.5% to 5% in HMDP and 0.04% to 0.4% in NFBC1966), which was further scaled with a random factor draw from a uniform distribution U(0.8, 1). The simulated effects were added back
