Descriptive statistics

The table below shows the descriptive statistics of all analyses variables. The overall sample size is 10000. There were 17.79 % cases with missing data. Multiple imputation was used to impute missing data (Rubin, 2004) and 17 datasets were imputed using the R package MICE (van Buuren, 2011).

Table. Descriptive statistics of continuous variables


Variables	N	Mean	SD	Median	IQR

y	8993	2.99193	1.04271	3.18736	1.98052
m1	9822	0.09971	0.14106	0.10198	0.20795
m2	9900	0.24007	0.27719	0.24324	0.48207
m3	9893	0.56540	0.62228	0.59094	1.13206
x	9498	0.50368	0.50001	1.00000	1.00000
c	10000	0.00003	0.10025	0.00015	0.13596

Regression analysis

The table below shows the estimates from the key regression models for the mediation analysis.

The outcome variable, y, was modelled with regression
The mediator, m1, was modelled with regression
The mediator, m2, was modelled with regression
The mediator, m3, was modelled with regression

The mediator models indicated that the exposure variable, x, was

significantly associated with the mediator, m1, b = 0.19961, 95% CI = ( 0.19570, 0.20351).
significantly associated with the mediator, m2, b = 0.48133, 95% CI = ( 0.47606, 0.48660).
significantly associated with the mediator, m3, b = 1.13217, 95% CI = ( 1.12243, 1.14191).

After accounting for the effect of the mediators , the outcome model indicated that the treatment variable, x, was significantly associated with y, b = 0.80356, 95% CI = (0.79131, 0.81582).
The outcome model also indicated that

m1 is significantly associated with the outcome, y, b = 0.49540, 95% CI = (0.45996, 0.53085).
m2 is significantly associated with the outcome, y, b = 0.60971, 95% CI = (0.57822, 0.64119).
m3 is significantly associated with the outcome, y, b = 0.69465, 95% CI = (0.67391, 0.71539).

The effect of c was adjusted for in the above analyses.

Table. Results from key regression analyses.

	m1			m2			m3			y
Variables	b	95% CI	p-value	b	95% CI	p-value	b	95% CI	p-value	b	95% CI	p-value
(Intercept)	-0.00081	(-0.00358, 0.00196)	0.566	-0.00213	(-0.00587, 0.00161)	0.264	-0.00349	(-0.01040, 0.00343)	0.323	1.99912***	(1.99612, 2.00211)	0.000
c	0.10084***	( 0.08136, 0.12031)	0.000	0.30100***	( 0.27468, 0.32732)	0.000	0.70530***	( 0.65663, 0.75397)	0.000	0.40430***	(0.38214, 0.42646)	0.000
x	0.19961***	( 0.19570, 0.20351)	0.000	0.48133***	( 0.47606, 0.48660)	0.000	1.13217***	( 1.12243, 1.14191)	0.000	0.80356***	(0.79131, 0.81582)	0.000
m1	-	-	-	-	-	-	-	-	-	0.49540***	(0.45996, 0.53085)	0.000
m2	-	-	-	-	-	-	-	-	-	0.60971***	(0.57822, 0.64119)	0.000
m3	-	-	-	-	-	-	-	-	-	0.69465***	(0.67391, 0.71539)	0.000

***p <.001;**p <.01;*p <.05.

Mediation analysis

Mediation analysis was performed based on the counter-factual framework and the interventional effect (Vansteelandt and Daniel, 2017; Chan and Leung, 2020). The analysis was conducted in R using the intmed package (Chan and Leung, 2020) with 17000 simulations.
Results from the mediation analysis indicated that

the indirect effect through m1 was statistically significant, p = 0.000; 4.98664% of the total effect was mediated through m1.
the indirect effect through m2 was statistically significant, p = 0.000; 14.80209% of the total effect was mediated through m2.
the indirect effect through m3 was statistically significant, p = 0.000; 39.66936% of the total effect was mediated through m3.
the direct effect was statistically significant, p = 0.000.
the total effect was statistically significant, p = 0.000.

Table. Mediation analysis results.

	Estimates	95% CI	p-value
Indirect effect mediated through m1	0.09886***	(0.09145, 0.10619)	0.000
Indirect effect mediated through m2	0.29351***	(0.27838, 0.30893)	0.000
Indirect effect mediated through m3	0.78638***	(0.76187, 0.81097)	0.000
Direct effect	0.80350***	(0.79126, 0.81565)	0.000
Total effect	1.98234***	(1.97053, 1.99416)	0.000
Proportion of effect mediated through m1	0.04987
Proportion of effect mediated through m2	0.14802
Proportion of effect mediated through m3	0.39669

***p < .001;**p < .05***p < .05.