Table 1.

Comparison of mIHT and multiple uIHT implemented in MendelIHT, CAA implemented in mv-PLINK, and mvLMM implemented in GEMMA^a.

	Time (s)	Plei power	Indep power	FP
Set 1: (2 traits, $k_{\mathit{true}}=10,\hspace{0.17em}{k}_{\mathit{indep}}=4,\hspace{0.17em}{k}_{\mathit{plei}}=3$)
mIHT	$164.6\pm 69.3$	$0.92\pm 0.16$	$0.76\pm 0.2$	$3.7\pm 6.4$
uIHT	$114.9\pm 48.6$	$0.93\pm 0.16$	$0.72\pm 0.2$	$1.4\pm 3.7$
CCA	$152.6\pm 57.3$	$0.96\pm 0.14$	$0.78\pm 0.2$	$77.8\pm 0.2$
mvLMM	$307.7\pm 121.4$	$0.95\pm 0.15$	$0.76\pm 0.2$	$42.8\pm 18.5$
Set 2: (3 traits, $k_{\mathit{true}}=20,\hspace{0.17em}{k}_{\mathit{indep}}=10,\hspace{0.17em}{k}_{\mathit{plei}}=5$)
mIHT	$214.4\pm 100.1$	$0.91\pm 0.12$	$0.75\pm 0.14$	$5.7\pm 6.0$
uIHT	$169.6\pm 81.9$	$0.86\pm 0.16$	$0.72\pm 0.16$	$2.4\pm 2.5$
CCA	$226.8\pm 101.9$	$0.95\pm 0.09$	$0.79\pm 0.15$	$125.3\pm 55.3$
mvLMM	$449.9\pm 221.7$	$0.93\pm 0.1$	$0.75\pm 0.16$	$66.1\pm 22.8$
Set 3: (5 traits, $k_{\mathit{true}}=30,\hspace{0.17em}{k}_{\mathit{indep}}=16,\hspace{0.17em}{k}_{\mathit{plei}}=7$)
mIHT	$227.9\pm 41.1$	$0.93\pm 0.09$	$0.73\pm 0.12$	$5.9\pm 4.6$
uIHT	$213.8\pm 45.7$	$0.90\pm 0.11$	$0.69\pm 0.12$	$3.2\pm 3.8$
CCA	$371.5\pm 34.0$	$0.96\pm 0.07$	$0.75\pm 0.11$	$173.2\pm 54.9$
mvLMM	$1135.3\pm 125.5$	$0.94\pm 0.09$	$0.71\pm 0.11$	$93.6\pm 22.7$
Set 4: (10 traits, $k_{\mathit{true}}=10,\hspace{0.17em}{k}_{\mathit{indep}}=4,\hspace{0.17em}{k}_{\mathit{plei}}=3$)
mIHT	$278.8\pm 53.0$	$0.97\pm 0.09$	$0.74\pm 0.20$	$2.2\pm 2.0$
uIHT	$245.8\pm 34.8$	$0.96\pm 0.11$	$0.70\pm 0.23$	$3.1\pm 6.4$
CCA	$985.1\pm 97.5$	$0.99\pm 0.06$	$0.78\pm 0.20$	$64.6\pm 30.5$
mvLMM	$8067.4\pm 3900.8$	$0.99\pm 0.06$	$0.74\pm 0.18$	$41.8\pm 16.4$
Set 5: (50 traits, $k_{\mathit{true}}=20,\hspace{0.17em}{k}_{\mathit{indep}}=10,\hspace{0.17em}{k}_{\mathit{plei}}=5$)
mIHT	$1892.2\pm 419.0$	$0.93\pm 0.12$	$0.75\pm 0.14$	$2.9\pm 2.5$
uIHT	$1336.9\pm 310.2$	$0.92\pm 0.11$	$0.72\pm 0.12$	$7.6\pm 5.9$
CCA	$26\hspace{0.17em}589.1\pm 907.7$(*)	NA	NA	NA
mvLMM	NA	NA	NA	NA
Set 6: (100 traits, $k_{\mathit{true}}=30,\hspace{0.17em}{k}_{\mathit{indep}}=16,\hspace{0.17em}{k}_{\mathit{plei}}=7$)
mIHT	$3699.3\pm 410.4$	$0.91\pm 0.11$	$0.71\pm 0.11$	$2.8\pm 2.1$
uIHT	$2353.8\pm 212.3$	$0.92\pm 0.11$	$0.7\pm 0.1$	$10.7\pm 4.3$
CCA	NA	NA	NA	NA
mvLMM	NA	NA	NA	NA

^aTraits were simulated consistent with the Chromosome 1 SNPs of the NFBC1966 data. Plei power is power for pleiotopic SNPs, Indep power is power for independent SNPs, and FP is the total number of FPs, which potentially includes variants in high LD. Fig. 1 repeats the same simulation with LD-pruning. Displayed numbers are mean $\pm$ SDs. $k_{\mathit{true}}$ is the total number of non-zero entries in $\mathbf{B}$, $k_{\mathit{indep}}$ is the number of independent SNPs affecting only one trait, and $k_{\mathit{plei}}$ is the number of pleiotropic SNPs affecting two traits. These numbers satisfy $k_{\mathit{true}}=2\times k_{\mathit{plei}}+k_{\mathit{indep}}$. Each simulation relied on 100 replicates. NA: >24 h. (*) Only two replicates contribute to timing.