TABLE 3.

Comparison of the pIVW estimator (${\lambda }_{opt}=1$) with other competing MR methods. The true causal effect $\beta =0.5$. No horizontal pleiotropy exists ($\tau =0$). The IV selection threshold $\delta =\sqrt{2\log p}$. The simulation is based on 10,000 replicates. Bias (%): bias divided by β; CP (%): coverage probability of the 95% confidence interval; SE: empirical standard error

${\eta }_{\delta }$	Method	Bias	SE	CP
6.76	IVW	−7.3	0.122	93.4
	MR‐Egger	−41.9	0.376	89.3
	MR‐Median	−11.6	0.140	95.1
	MR‐RAPS	1.4	0.137	95.8
	dIVW	3.2	0.144	96.0
	pIVW	−0.1	0.136	95.3
10.26	IVW	−7.9	0.079	91.4
	MR‐Egger	−43.6	0.207	79.2
	MR‐Median	−12.2	0.097	93.0
	MR‐RAPS	0.7	0.088	95.5
	dIVW	1.4	0.090	95.5
	pIVW	0.1	0.088	95.1
17.84	IVW	−7.9	0.049	87.4
	MR‐Egger	−48.6	0.130	51.2
	MR‐Median	−12.5	0.062	88.3
	MR‐RAPS	0.4	0.055	94.9
	dIVW	0.7	0.056	95.0
	pIVW	0.2	0.055	94.7