. 2024 Jul 24;111(8):1736–1749. doi: 10.1016/j.ajhg.2024.06.012

Table 2.

Simulation results evaluating the performance of mintMR and competing methods in different scenarios

	Number of IVs			Probability of QTL effect being consistent across QTL and GWAS sample			Number of tissues for each exposure
	15	25	100	0.8	0.5	0.2	5	10	15

Power

mintMR	0.734	0.822	0.932	0.867	0.789	0.660	0.553	0.713	0.739
mintMR_oracle	0.764	0.861	0.964	0.898	0.852	0.746	0.586	0.810	0.900
mintMR_single-gene	0.547^∗	0.789^∗	0.963	0.751^∗	0.712^∗	0.527^∗	0.497^∗	0.538^∗	0.583^∗
IVW+metaIV	0.351^∗	0.352^∗	0.530	0.299^∗	0.388^∗	0.399^∗	0.321^∗	0.286^∗	0.281^∗
Egger	0.236^∗	0.254^∗	0.220	0.367^∗	0.289^∗	0.264^∗	0.240^∗	0.180^∗	0.192^∗
MVMR-IVW	0.444^∗	0.774	0.969	0.682^∗	0.572^∗	0.436	0.316^∗	0.302^∗	0.487
MVMR-Egger	0.383^∗	0.729	0.898	0.562^∗	0.495	0.407	0.266^∗	0.326^∗	0.404
MVMR-Lasso	0.631^∗	0.783	0.969	0.793^∗	0.679^∗	0.443	0.612^∗	0.364^∗	0.493
MVMR-Median	0.526^∗	0.745^∗	0.920^∗	0.723^∗	0.671^∗	0.500	0.418^∗	0.225	0.480^∗
MVMR-Robust	0.276	0.730	0.961	0.513	0.432	0.324	0.175	0.190	0.407

Type I error rate

mintMR	0.049	0.055	0.041	0.053	0.066	0.060	0.052	0.037	0.062
mintMR_oracle	0.049	0.051	0.056	0.049	0.054	0.050	0.048	0.050	0.048
mintMR_single-gene	0.115^∗	0.109^∗	0.059	0.236^∗	0.152^∗	0.194^∗	0.174^∗	0.235^∗	0.126^∗
IVW+metaIV	0.145^∗	0.144^∗	0.093	0.148^∗	0.156^∗	0.168^∗	0.146^∗	0.157^∗	0.125^∗
Egger	0.134^∗	0.112^∗	0.074	0.109^∗	0.110^∗	0.127^∗	0.138^∗	0.124^∗	0.105^∗
MVMR-IVW	0.122^∗	0.064	0.055	0.122^∗	0.106^∗	0.067	0.126^∗	0.122^∗	0.081
MVMR-Egger	0.122^∗	0.063	0.055	0.120^∗	0.098	0.064	0.126^∗	0.153^∗	0.084
MVMR-Lasso	0.194^∗	0.068	0.057	0.188^∗	0.129^∗	0.069	0.303^∗	0.145^∗	0.081
MVMR-Median	0.114^∗	0.116^∗	0.100^∗	0.172^∗	0.112^∗	0.069	0.135^∗	0.076	0.103^∗
MVMR-Robust	0.066	0.047	0.051	0.067	0.052	0.036	0.072	0.062	0.060

When varying the number of IVs, the proportion of variation in outcome explained by UHP effect is 0.1. The causal effects are generated from $N (0, 0.01)$ . The probability of QTL effect being consistent across QTL and GWAS samples is 0.8. Five tissues are generated for each exposure. When decreasing the probability of QTL effect being consistent, the causal effects are generated from $N (0, 0.02)$ . We simulated 15 IVs across 5 tissues for each exposure. When the number of tissues for each exposure increased from 5, 10, to 20, we simulated 15, 25, and 45 IVs, respectively. The probability of consistency is 0.8. Causal effects are generated from $N (0, 0.01)$ . Results are asterisked (^∗) for methods unable to control type I error rates (≥0.1).