Table A4.

Investigation into bias of summary statistic estimator.

		β X=0.2			β X=0
	α	Median	Coverage	Power	Median	Coverage	Power
Crude weights
β U=+1	0.05	0.348	88.2	58.4	0.146	82.8	17.2
	0.10	0.248	94.5	78.2	0.047	91.7	8.3
	0.20	0.213	96.6	99.3	0.012	94.0	6.0
β U=−1	0.05	0.056	77.9	7.3	−0.149	83.0	17.0
	0.10	0.152	88.3	53.0	−0.047	91.9	8.1
	0.20	0.188	91.8	99.5	−0.013	94.2	5.8
External weights
β U=+1	0.05	0.144	93.7	15.5	−0.001	95.2	4.8
	0.10	0.183	94.2	52.4	0.000	95.1	4.9
	0.20	0.196	94.4	97.9	0.000	94.9	5.1
β U=−1	0.05	0.150	92.8	19.8	0.002	94.8	5.2
	0.10	0.182	93.7	67.7	0.000	95.2	4.8
	0.20	0.196	94.1	99.7	0.000	95.2	4.8

Median estimates over 10000 simulations from summary statistic method with causal effect β _X=0.2 and β _X=0, coverage (%) of nominal 95% confidence interval for the causal parameter and empirical power (%) based on nominal 95% confidence interval to detect a causal effect from simulation study with 15 uncorrelated instrumental variables (IVs) varying the direction of confounding (β _U) and average strength of IV (α) with crude weights and with external weights corresponding to an independent sample of size 5000.