An empirical evaluation of approximate and exact regression-based causal mediation approaches for a binary outcome and a continuous or a binary mediator for case-control study designs

Table 1 Comparison of approaches for the estimation of natural effects on the odds ratio scale for Scenario 1 with a continuous mediator (based on 1000 data sets of size \(n=1000\))

Effect	Approach	True value	Mean	Bias	Relative bias (%)	SD	RMSE	CP (%) delta	CP (%) boot
NDE	Approx_Naive	1.525	1.557	0.032	2.094	0.203	0.205	95.3	94.8
	Approx_C	1.525	1.558	0.032	2.129	0.204	0.207	95.2	95.0
	Approx_IPW	1.525	1.558	0.033	2.166	0.206	0.208	95.4	94.9
	Exact_Naive	1.525	1.541	0.016	1.031	0.206	0.206	95.1	95.3
	Exact_IPW	1.525	1.556	0.030	1.985	0.206	0.208	95.7	94.9
	Unified	1.525	1.558	0.033	2.135	0.204	0.207	95.2	-
NIE	Approx_Naive	1.064	1.073	0.009	0.838	0.046	0.047	95.9	94.2
	Approx_C	1.064	1.060	-0.004	-0.383	0.035	0.035	98.9	95.8
	Approx_IPW	1.064	1.062	-0.002	-0.158	0.037	0.037	98.6	95.7
	Exact_Naive	1.064	1.072	0.008	0.746	0.045	0.046	95.6	94.8
	Exact_IPW	1.064	1.062	-0.002	-0.181	0.037	0.037	98.7	95.7
	Unified	1.064	1.060	-0.004	-0.403	0.034	0.035	97.2	-
TE	Approx_Naive	1.623	1.669	0.046	2.830	0.214	0.219	95.5	95.2
	Approx_C	1.623	1.649	0.026	1.621	0.208	0.210	96.1	95.6
	Approx_IPW	1.623	1.653	0.031	1.883	0.211	0.213	96.1	95.4
	Exact_Naive	1.623	1.649	0.026	1.604	0.208	0.210	96.1	95.4
	Exact_IPW	1.623	1.650	0.027	1.674	0.210	0.212	96.2	95.4
	Unified	1.623	1.649	0.026	1.607	0.208	0.210	96.1	-

boot Bootstrap, CP Coverage probability, NDE Natural direct effect, NIE Natural indirect effect, RMSE Root mean squared error, SD Standard deviation, TE Total effect

ISSN: 1471-2288