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 12 Estimated conditional total effect (TE) and natural direct effect (NDE) of long-term use of oral contraceptives on invasive ovarian cancer, with natural indirect effect (NIE) via lifetime number of ovulatory cycles

Effect	Approach	Estimate	SE	95% CI
NDE	Approx_Naive	0.655	0.174	0.389, 1.102
	Approx_C	0.657	0.170	0.396, 1.092
	Approx_IPW	0.650	0.152	0.411, 1.027
	Exact_Naive	0.659	0.171	0.396, 1.097
	Exact_IPW	0.650	0.152	0.411, 1.029
	Unified	0.654	0.158	0.407, 1.049
NIE	Approx_Naive	0.870	0.166	0.598, 1.264
	Approx_C	0.876	0.159	0.614, 1.249
	Approx_IPW	0.878	0.138	0.646, 1.194
	Exact_Naive	0.870	0.165	0.600, 1.262
	Exact_IPW	0.878	0.138	0.645, 1.196
	Unified	0.863	0.144	0.623, 1.196
TE	Approx_Naive	0.569	0.093	0.413, 0.785
	Approx_C	0.576	0.094	0.418, 0.794
	Exact_Naive	0.573	0.093	0.417, 0.788
	Approx_IPW	0.571	0.094	0.414, 0.787
	Exact_IPW	0.571	0.094	0.414, 0.787
	Unified	0.564	0.092	0.410, 0.776

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