Comparison of logistic-regression based methods for simple mediation analysis with a dichotomous outcome variable

Rijnhart, Judith J. M.; Twisk, Jos W. R.; Eekhout, Iris; Heymans, Martijn W.

doi:10.1186/s12874-018-0654-z

BMC Medical Research Methodology

Table 3 Bias and efficiency yielded by the three compared methods for models with a dichotomous mediator

From: Comparison of logistic-regression based methods for simple mediation analysis with a dichotomous outcome variable

			Multiple regression and SEM						Potential outcomes
			Crude		y-standardization		Full-standardization
M prev	Y prev		bias	MSE	bias	MSE	bias	MSE	bias	MSE
0.5	0.5	Indirect effect							0.000	0.000
		ab	0.002	0.008	0.000	0.001	0.000	0.000
		c-c’	−0.287	0.083	−0.054	0.003	0.006	0.000
		Proportion mediated							0.001	0.001
		ab/(ab + c’)	−0.003	0.005	−0.136	0.021	−0.235	0.057
		ab/c	0.167	0.048	−0.096	0.014	−0.236	0.057
		1-(c’/c)	−0.266	0.072	−0.254	0.066	−0.254	0.066
	0.3	Indirect effect							−0.001	0.000
		ab	0.003	0.010	−0.001	0.001	0.000	0.000
		c-c’	−0.288	0.083	−0.055	0.003	0.007	0.000
		Proportion mediated							0.001	0.001
		ab/(ab + c’)	−0.004	0.006	−0.136	0.022	−0.235	0.057
		ab/c	0.168	0.054	−0.095	0.016	−0.235	0.057
		1-(c’/c)	−0.265	0.071	−0.254	0.066	−0.254	0.066
	0.1	Indirect effect							0.002	0.001
		ab	0.016	0.021	−0.003	0.001	0.002	0.000
		c-c’	−0.284	0.081	−0.052	0.003	−0.004	0.000
		Proportion mediated							0.004	0.002
		ab/(ab + c’)	−0.001	0.012	−0.132	0.024	−0.230	0.056
		ab/c	0.187	0.087	−0.087	0.021	−0.231	0.057
		1-(c’/c)	−0.261	0.070	−0.248	0.064	−0.248	0.064
0.3	0.5	Indirect effect							−0.001	0.001
		ab	−0.001	0.020	−0.001	0.001	−0.000	0.000
		c-c’	−0.299	0.081	−0.062	0.003	− 0.009	0.000
		Proportion mediated							−0.001	0.001
		ab/(ab + c’)	−0.006	0.013	−0.138	0.025	−0.247	0.062
		ab/c	0.171	0.086	−0.093	0.022	−0.246	0.062
		1-(c’/c)	−0.283	0.070	−0.272	0.066	−0.272	0.066
	0.3	Indirect effect							−0.001	0.001
		ab	−0.001	0.011	−0.001	0.001	0.000	0.000
		c-c’	−0.294	0.087	−0.060	0.004	−0.007	0.000
		Proportion mediated							0.001	0.001
		ab/(ab + c’)	−0.003	0.007	−0.135	0.022	−0.244	0.061
		ab/c	0.176	0.061	−0.090	0.016	−0.244	0.061
		1-(c’/c)	−0.274	0.076	− 0.264	0.071	−0.264	0.071
	0.1	Indirect effect							0.003	0.001
		ab	0.012	0.010	0.002	0.001	0.001	0.000
		c-c’	−0.283	0.090	−0.054	0.004	−0.001	0.000
		Proportion mediated							0.004	0.003
		ab/(ab + c’)	−0.004	0.006	− 0.134	0.022	−0.242	0.062
		ab/c	0.179	0.054	−0.090	0.015	−0.244	0.062
		1-(c’/c)	−0.260	0.081	−0.252	0.075	−0.252	0.075
0.1	0.5	Indirect effect							0.004	0.001
		ab	0.013	0.026	0.002	0.002	−0.018	0.000
		c-c’	−0.333	0.111	−0.082	0.007	−0.032	0.001
		Proportion mediated							0.004	0.001
		ab/(ab + c’)	−0.006	0.011	−0.137	0.025	−0.284	0.082
		ab/c	0.223	0.113	−0.066	0.020	−0.281	0.081
		1-(c’/c)	−0.332	0.111	−0.326	0.107	−0.326	0.107
	0.3	Indirect effect							0.003	0.001
		ab	0.009	0.025	0.002	0.002	−0.018	0.000
		c-c’	−0.328	0.108	−0.080	0.006	−0.030	0.001
		Proportion mediated							0.005	0.001
		ab/(ab + c’)	−0.005	0.013	−0.135	0.025	−0.283	0.082
		ab/c	0.225	0.121	−0.065	0.022	−0.281	0.081
		1-(c’/c)	−0.323	0.105	−0.318	0.102	−0.318	0.102
	0.1	Indirect effect							0.003	0.001
		ab	0.002	0.033	−0.001	0.002	−0.018	0.001
		c-c’	−0.319	0.102	−0.076	0.006	−0.026	0.001
		Proportion mediated							0.003	0.002
		ab/(ab + c’)	−0.024	0.027	−0.145	0.033	−0.286	0.084
		ab/c	0.193	0.130	−0.081	0.031	−0.285	0.084
		1-(c’/c)	−0.310	0.098	−0.307	0.096	−0.307	0.096

Abbreviations: SEM structural equation modeling, M prev mediator prevalence, Y prev outcome prevalence, MSE mean squared error

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