TABLE 2.

Average causal effect estimates, estimated SEs, root mean squared errors, empirical Type I error rates (𝜃 = 0), and empirical coverage (𝜃 = 0.3) for the three simulation scenarios and a variety of MR methods

	Causal effect 𝜽 = 0				Causal effect 𝜽 = 0.3
Method	Mean	SE	RMSE	Type I	Mean	SE	RMSE	Coverage
Balanced pleiotropy
IVW	0.000	0.022	0.022	0.057	0.296	0.022	0.023	0.942
MR-Egger	−0.003	0.065	0.065	0.055	0.265	0.066	0.077	0.912
Median	0.000	0.010	0.010	0.061	0.294	0.012	0.014	0.915
Mode	0.000	0.016	0.012	0.011	0.288	0.020	0.019	0.954
Lasso	0.000	0.007	0.007	0.089	0.296	0.008	0.010	0.861
MR-Presso	0.000	0.007	0.008	0.086	0.296	0.010	0.012	0.884
MR-Raps	0.000	0.019	0.019	0.048	0.300	0.020	0.020	0.951
ConMix	0.000	–	0.008	0.218	0.298	–	0.011	0.778
JAM-MR	0.000	0.007	0.008	0.074	0.294	0.009	0.013	0.851
Oracle	0.000	0.007	0.007	0.045	0.296	0.008	0.009	0.919
Directional pleiotropy, InSIDE satisfied
IVW	0.208	0.019	0.208	1.000	0.503	0.019	0.204	0.000
MR-Egger	0.000	0.056	0.058	0.067	0.264	0.057	0.068	0.910
Median	0.052	0.011	0.053	0.999	0.358	0.013	0.059	0.008
Mode	0.000	0.014	0.011	0.012	0.290	0.018	0.017	0.961
Lasso	0.028	0.007	0.029	0.948	0.339	0.008	0.041	0.021
MR-Presso	0.077	0.011	0.078	1.000	0.396	0.013	0.098	0.000
MR-Raps	0.170	0.019	0.171	1.000	0.472	0.020	0.173	0.000
ConMix	0.001	–	0.008	0.183	0.302	–	0.011	0.771
JAM-MR	0.005	0.007	0.009	0.106	0.301	0.009	0.012	0.897
Oracle	0.000	0.007	0.006	0.044	0.296	0.008	0.009	0.919
Directional pleiot	ropy, InSIDE	violated
IVW	0.372	0.022	0.372	1.000	0.668	0.023	0.369	0.000
MR-Egger	0.705	0.060	0.707	1.000	0.978	0.062	0.680	0.000
Median	0.167	0.018	0.175	1.000	0.496	0.021	0.204	0.000
Mode	0.000	0.017	0.011	0.016	0.288	0.016	0.018	0.929
Lasso	0.045	0.008	0.047	0.996	0.366	0.009	0.068	0.000
MR-Presso	0.204	0.017	0.206	1.000	0.517	0.018	0.218	0.000
MR-Raps	0.338	0.024	0.339	1.000	0.640	0.024	0.340	0.000
ConMix	0.001	–	0.009	0.220	0.299	–	0.010	0.813
JAM-MR	0.002	0.007	0.008	0.074	0.296	0.009	0.011	0.899
Oracle	0.000	0.007	0.007	0.053	0.296	0.008	0.009	0.919