Estimating the natural indirect effect and the mediation proportion via the product method

Cheng, Chao; Spiegelman, Donna; Li, Fan

doi:10.1186/s12874-021-01425-4

BMC Medical Research Methodology

Table 3 Simulation results for Case #1: continuous outcome and continuous mediator

From: Estimating the natural indirect effect and the mediation proportion via the product method

			\(\widehat {\text {NIE}}\)				\(\widehat {\text {MP}}\)
N	MP	TE	Bias(%)	CR ^(d)	CR ^(b)	VR	Bias(%)	CR ^(d)	CR ^(b)	VR
150	0.05	0.25	-16.4	99.2	96.4	0.998	-27.5	99.2	98.8	0.000
		0.5	-15.1	96.5	95.7	0.992	-14.1	96.9	96.5	0.058
		1	-10.5	92.2	94.7	0.993	-9.8	92.6	95.1	0.949
	0.2	0.25	-10.5	92.2	94.7	0.993	-19.7	90.6	97.3	0.000
		0.5	-6.2	92.5	94.8	1.001	-2.8	92.9	96.4	0.092
		1	-2.1	94.8	94.9	1.012	-1.7	95.7	95.4	0.944
	0.5	0.25	-4.7	93.2	94.8	1.007	-14.1	89.1	97.0	0.000
		0.5	-1.6	95.1	95.0	1.012	-0.4	96.0	97.0	0.026
		1	-0.1	95.5	94.9	1.013	0.2	97.5	95.3	0.710
500	0.05	0.25	-4.4	96.0	94.4	0.997	-3.5	97.8	96.6	0.002
		0.5	-3.5	94.7	94.2	0.988	-3.4	95.3	94.5	0.855
		1	-2.6	93.1	94.2	0.983	-2.8	93.4	94.4	0.948
	0.2	0.25	-2.6	93.1	94.2	0.983	-1.5	92.1	97.0	0.001
		0.5	-1.5	93.6	94.5	0.982	-0.8	94.4	94.8	0.801
		1	-0.2	94.5	94.5	0.981	-0.1	94.7	94.6	0.945
	0.5	0.25	-0.9	94.0	94.5	0.980	-0.4	92.3	97.5	0.000
		0.5	-0.1	94.7	94.3	0.982	0.1	95.5	94.9	0.770
		1	0.6	94.5	94.5	0.983	0.0	95.6	94.7	0.915
1000	0.05	0.25	-4.0	95.4	94.7	0.969	-3.2	97.0	95.4	0.724
		0.5	-2.2	94.8	94.7	0.969	-2.8	95.2	95.1	0.924
		1	-2.1	94.1	94.8	0.971	-1.9	94.0	94.7	0.967
	0.2	0.25	-2.1	94.1	94.8	0.971	-1.1	93.5	96.3	0.580
		0.5	-1.1	94.2	94.6	0.981	-1.2	94.2	94.8	0.923
		1	-0.9	94.9	94.8	0.986	-0.8	94.6	94.4	0.981
	0.5	0.25	-1.1	94.4	94.6	0.983	-0.5	92.8	96.6	0.441
		0.5	-0.5	95.0	94.9	0.987	-0.5	94.9	94.6	0.916
		1	-0.3	94.8	94.7	0.988	-0.4	95.0	94.5	0.966
5000	0.05	0.25	-0.5	94.8	94.8	0.990	0.3	95.5	94.8	0.961
		0.5	-0.2	94.9	95.0	0.995	-0.3	95.4	95.0	0.990
		1	-0.2	95.0	95.1	1.007	-0.3	95.0	95.1	1.006
	0.2	0.25	-0.2	95.0	95.1	1.007	0.1	95.6	95.1	0.936
		0.5	-0.1	95.0	95.2	1.027	-0.1	95.1	95.3	1.004
		1	0.0	95.3	95.2	1.038	0.0	95.1	95.1	1.031
	0.5	0.25	0.0	95.3	95.5	1.032	0.1	95.0	94.7	0.920
		0.5	-0.1	95.3	95.2	1.040	0.0	95.2	95.0	0.995
		1	0.0	95.4	95.2	1.041	0.0	95.3	95.4	1.022

¹Note: Bias(%), CR ^(d), CR ^(b), and VR denote the median percent bias, 95% confidence interval coverage rate of multivariate delta method, 95% confidence interval coverage rate of percentile bootstrap method, and mediation variance ratio, respectively. The coverage rates outside the 95% confidence boundary, i.e., \(q \pm 1.96\times \sqrt {\frac {q(1-q)}{B}}\), were highlighted in bold, where q denotes the nominal confidence interval threshold (95%) and B denotes the number of replication (5,000). The median percent bias was calculated as the median of the ratio of bias to the true value over 5,000 replications, i.e., \(\text {Bias(\%)}=median(\frac {\hat {p}-p}{p}) \times 100\%\), where p denotes the true value of the causal mediation measure, and \(\hat {p}\) is the point estimate of the simulated causal mediation measure. The median variance ratio is defined by the ratio of median delta-method variance estimators across 5,000 replications to the empirical variance of causal mediation measure estimates from the 5,000 replications

Back to article page

ISSN: 1471-2288

Contact us

General enquiries: journalsubmissions@springernature.com