Table 1.

Performance of cis‐MR methods in simulations for various values of the causal effect parameter $\theta$, using genetic variants from two gene regions (SHBG and HMGCR) and “strong” genetic instruments (corresponding F statistics $>10$)

		$\theta =0$			$\theta =0.05$				$\theta =0.1$
Method		$\hat{\theta }$	$se\left(\hat{\theta }\right)$	Type I	$\hat{\theta }$	$se\left(\hat{\theta }\right)$	Cov	Power	$\hat{\theta }$	$se\left(\hat{\theta }\right)$	Cov
SHBG region
Top SNP	—	0.000	0.019	0.051	0.050	0.019	0.956	0.731	0.096	0.020	0.927
Pruning	$\rho =0.1$	−0.002	0.016	0.051	0.048	0.017	0.938	0.837	0.096	0.017	0.936
	$\rho =0.3$	−0.001	0.014	0.049	0.048	0.014	0.949	0.923	0.096	0.015	0.932
	$\rho =0.5$	−0.001	0.013	0.051	0.047	0.014	0.943	0.941	0.095	0.014	0.927
	$\rho =0.7$	−0.001	0.013	0.050	0.046	0.013	0.939	0.940	0.092	0.014	0.901
	$\rho =0.9$	0.000	0.012	0.047	0.043	0.013	0.912	0.928	0.086	0.013	0.796
PCA	$k=0.99$	−0.001	0.015	0.063	0.049	0.015	0.954	0.914	0.099	0.016	0.938
	$k=0.999$	0.000	0.014	0.050	0.048	0.014	0.941	0.933	0.096	0.015	0.935
JAM	$\rho =0.6$	−0.001	0.014	0.048	0.048	0.014	0.954	0.935	0.095	0.015	0.938
	$\rho =0.8$	0.000	0.014	0.049	0.047	0.014	0.957	0.934	0.095	0.015	0.939
	$\rho =0.9$	0.000	0.014	0.041	0.048	0.014	0.955	0.932	0.094	0.015	0.935
	$\rho =0.95$	0.000	0.014	0.045	0.047	0.014	0.956	0.933	0.094	0.015	0.933
F‐LIML	—	0.000	0.014	0.066	0.051	0.015	0.942	0.936	0.100	0.016	0.953
CLR	—	—	—	0.054	—	—	0.947	0.926	—	—	0.958
HMGCR region
Top SNP	—	0.001	0.018	0.048	0.049	0.019	0.953	0.776	0.099	0.019	0.924
Pruning	$\rho =0.1$	0.001	0.018	0.048	0.049	0.019	0.953	0.776	0.099	0.019	0.924
	$\rho =0.3$	0.001	0.017	0.048	0.048	0.018	0.948	0.795	0.097	0.018	0.928
	$\rho =0.5$	0.000	0.017	0.056	0.047	0.017	0.953	0.825	0.096	0.017	0.932
	$\rho =0.7$	0.000	0.016	0.052	0.046	0.016	0.938	0.820	0.093	0.017	0.917
	$\rho =0.9$	0.000	0.015	0.057	0.042	0.015	0.924	0.766	0.084	0.016	0.802
PCA	$k=0.99$	0.000	0.017	0.049	0.049	0.017	0.949	0.830	0.099	0.018	0.930
	$k=0.999$	0.000	0.016	0.052	0.048	0.017	0.953	0.826	0.098	0.017	0.934
JAM	$\rho =0.6$	0.001	0.017	0.047	0.048	0.018	0.957	0.789	0.096	0.018	0.935
	$\rho =0.8$	0.000	0.017	0.039	0.047	0.018	0.961	0.777	0.096	0.018	0.942
	$\rho =0.9$	0.000	0.017	0.039	0.047	0.018	0.957	0.777	0.096	0.018	0.939
	$\rho =0.95$	0.001	0.017	0.035	0.047	0.018	0.957	0.777	0.095	0.018	0.939
F‐LIML	—	0.000	0.017	0.064	0.050	0.017	0.945	0.850	0.101	0.019	0.946
CLR	—	—	—	0.055	—	—	0.947	0.834	—	—	0.945