To compare power between GEMMA and MTMM, we used real genotypes from the HMDP and NFBC1966 data, and we simulated phenotypes by adding genotype effects back to the original phenotypes15,17. Specifically, we first identified SNPs unassociated with the four phenotypes based on one-phenotype, two-phenotype and four-phenotype analyses (LRT p value > 0.1 in any of the 11 tests). We ordered the SNPs (76,780 in HMDP and 208,145 in NFBC1966) satisfying these criteria by their genomic location, and selected from them 10,000 evenly spaced SNPs to act as causal SNPs. For each causal SNP, we specified its effect size for the first trait (HDL) to explain a particular percentage of the phenotypic variance (proportion of variance explained, or PVE). Afterwards, we specified its effect for the second trait (TG) so that the proportion of variance in the second trait explained by the SNP equals to either 20% or 80% of the PVE in the first trait. We considered effect sizes for the two traits to be either in the same direction or in the opposite directions, and we added the simulated
