Table 4.

Comparison of allele score methods for correlated instrumental variables (IVs).

	α	R 2	F	Allele score using individual‐level data	Allele score using summarized data
Positive causal effect: β X=0.2
β U=+1	0.05	0.019	6.3	0.201 (0.116) [43.3]	0.201 (0.129) [34.9]
	0.10	0.062	22.2	0.201 (0.058) [87.2]	0.201 (0.065) [84.2]
	0.20	0.201	85.8	0.200 (0.029) [99.9]	0.200 (0.033) [99.8]
β U=−1	0.05	0.019	6.3	0.202 (0.117) [39.4]	0.202 (0.107) [48.0]
	0.10	0.062	22.2	0.199 (0.058) [91.8]	0.199 (0.053) [93.2]
	0.20	0.201	85.8	0.200 (0.029) [100.0]	0.200 (0.027) [100.0]
Null causal effect: β X=0
β U=+1	0.05	0.019	6.3	0.001 (0.116) [4.4]	0.001 (0.116) [4.8]
	0.10	0.062	22.2	0.000 (0.058) [4.7]	0.000 (0.058) [4.8]
	0.20	0.201	85.8	0.000 (0.029) [5.1]	0.000 (0.029) [5.0]
β U=−1	0.05	0.019	6.3	−0.002 (0.116) [4.3]	−0.002 (0.117) [4.8]
	0.10	0.062	22.2	0.000 (0.058) [5.0]	−0.001 (0.058) [5.0]
	0.20	0.201	85.8	0.000 (0.029) [5.1]	0.000 (0.029) [5.2]

Median estimates over 10000 simulations of β _X=0.2 or β _X=0 (median standard errors) [power (%) based on nominal 95% confidence interval] from simulation study with 15 correlated IVs varying direction of confounding (β _U) and average strength of IV (α; strength is also expressed by the mean values of the R ² and F statistics) using allele score methods calculated from individual‐level and summarized data, with equal weights.