Table 1.

Results from the main simulation study

Parameter	Method	Pruning	Mean	SD	Mean SE	Power
${\theta }_1$	MV‐IVW	Oracle	0.353	0.133	0.120	81.4
		0.4	0.304	0.164	0.147	57.4
		0.6	0.207	0.115	0.094	60.9
		0.8	−0.083	0.417	0.051	76.5
	MV‐LIML	Oracle	0.379	0.143	0.133	81.4
		0.4	0.340	0.188	0.163	58.9
		0.6	0.316	0.212	0.103	77.0
		0.8	0.083	2.372	0.179	78.8
	MV‐IVW‐PCA	–	0.296	0.130	0.119	69.3
	MV‐LIML‐PCA	–	0.347	0.152	0.130	74.5
${\theta }_2$	MV‐IVW	Oracle	−0.005	0.133	0.120	7.4
		0.4	−0.012	0.166	0.147	7.5
		0.6	−0.003	0.112	0.094	9.1
		0.8	0.037	0.408	0.051	75.4
	MV‐LIML	Oracle	−0.001	0.144	0.133	6.2
		0.4	−0.007	0.192	0.163	7.3
		0.6	0.006	0.186	0.103	20.2
		0.8	0.010	2.522	0.179	76.6
	MV‐IVW‐PCA	–	−0.013	0.129	0.119	7.1
	MV‐LIML‐PCA	–	−0.006	0.154	0.130	8.7
${\theta }_3$	MV‐IVW	Oracle	−0.545	0.132	0.120	98.6
		0.4	−0.487	0.166	0.148	87.6
		0.6	−0.315	0.139	0.094	86.9
		0.8	0.220	0.418	0.051	77.8
	MV‐LIML	Oracle	−0.576	0.142	0.134	98.8
		0.4	−0.531	0.190	0.164	88.6
		0.6	−0.451	0.212	0.103	92.6
		0.8	0.005	2.250	0.179	79.3
	MV‐IVW‐PCA	–	−0.476	0.130	0.119	96.1
	MV‐LIML‐PCA	–	−0.538	0.152	0.131	97.0

Note: Mean estimates, standard deviation (SD) of estimates, mean standard error (mean SE) of estimates, and empirical power of the 95% confidence interval to estimate ${\theta }_1=0.4$, ${\theta }_2=0$, and ${\theta }_3=-0.6$. We consider four methods, and various pruning thresholds for the MV‐IVW and MV‐LIML methods, plus an oracle setting in which only the 15 variants that truly affect the traits are included in the analysis.