Table 3.

Mean estimates from simulation 3: no horizontal pleiotropy and causal effect $\beta$ = 0.1 (10 000 simulations per scenario). Sample sizes $N_X$ and $N_Y$ are in thousands

Estimator	Statistic	N	Mean $\frac{{\overline{\mathit{F}}}_{\mathit{GX}}-1}{{\overline{\mathit{F}}}_{\mathit{GX}}}$ [%]; mean ${\mathit{I}}_{\mathit{GX}}^2$ [%]
			99.3; 94.8	99.3; 94.8	99.3; 94.8	99.7; 97.4	99.7; 97.4	99.7; 97.4	99.8; 98.7	99.8; 98.7	99.8; 98.7
		$N_X$	25	25	25	50	50	50	100	100	100
		$N_Y$	25	50	100	25	50	100	25	50	100
IVW	Beta		0.099	0.099	0.099	0.099	0.099	0.100	0.100	0.100	0.100
	SE		0.021	0.015	0.011	0.021	0.015	0.011	0.021	0.015	0.010
	Coverage (%)		96.5	96.5	96.4	96.7	96.3	96.7	96.1	96.7	97.0
	Power (%)		99.8	100.0	100.0	99.8	100.0	100.0	99.7	100.0	100.0
MR-Egger	Beta		0.096	0.096	0.096	0.098	0.098	0.098	0.099	0.099	0.099
	SE		0.045	0.032	0.023	0.046	0.032	0.023	0.046	0.033	0.023
	Coverage (%)		96.7	96.2	96.2	96.8	96.5	96.5	96.1	96.8	96.6
	Power (%)		53.7	82.1	97.8	54.2	84.0	98.1	54.9	83.9	98.5
Weighted	Beta		0.099	0.098	0.098	0.099	0.099	0.099	0.100	0.099	0.100
Median	SE		0.029	0.020	0.015	0.029	0.020	0.014	0.029	0.020	0.014
	Coverage (%)		97.3	97.1	97.1	97.1	97.2	97.4	97.0	97.4	97.9
	Power (%)		95.3	100.0	100.0	95.5	100.0	100.0	95.2	100.0	100.0
Simple	Beta		0.099	0.098	0.099	0.099	0.099	0.100	0.100	0.099	0.100
MBEa	SE		0.087	0.061	0.047	0.073	0.045	0.035	0.053	0.037	0.027
	Coverage (%)		99.0	99.1	98.9	99.1	99.0	99.1	98.8	98.8	99.2
	Power (%)		59.4	85.7	94.1	61.3	88.6	96.9	64.0	91.0	98.2
Weighted	Beta		0.097	0.097	0.097	0.098	0.098	0.099	0.099	0.098	0.099
MBEa	SE		0.079	0.055	0.043	0.065	0.040	0.031	0.044	0.031	0.022
	Coverage (%)		98.4	98.4	98.2	98.3	98.1	98.2	98.0	98.3	98.4
	Power (%)		75.2	90.9	94.7	77.5	94.5	97.1	80.0	96.7	98.7
Simple	Beta		0.099	0.098	0.099	0.099	0.099	0.100	0.100	0.099	0.100
MBE	SE		0.047	0.033	0.023	0.046	0.032	0.023	0.045	0.033	0.023
(under	Coverage (%)		98.8	98.9	98.8	99.1	98.9	99.0	98.8	98.9	99.1
NOME)a	Power (%)		64.1	91.1	98.8	64.2	91.4	99.2	64.9	91.7	99.3
Weighted	Beta		0.099	0.098	0.098	0.099	0.099	0.099	0.100	0.099	0.100
MBE	SE		0.038	0.027	0.019	0.038	0.026	0.019	0.037	0.026	0.018
(under	Coverage (%)		98.1	98.0	97.9	98.1	97.9	98.0	97.9	98.3	98.3
NOME)a	Power (%)		81.5	96.6	99.3	81.0	97.2	99.5	81.5	97.6	99.8

$N_X,$ sample size of the dataset used to estimate instrument-exposure associations$;\hspace{0.5em}{N}_Y,$ sample size of the dataset used to estimate instrument-outcome associations; IVW, inverse-variance weighting; SE, estimated standard error; NOME, NO Measurement Error; MBE, mode-based estimate.

^a$\varphi$ = 1.