Table 1.

Simulation results without post-treatment confounders

D’n	M	N	Z	NDE	$N\widehat{D}E$	NDE RMSE	Cov.	$r\widehat{r}$	NME	$N\widehat{M}E$	NME RMSE	Cov.	$r\widehat{r}$	NTE	$N\widehat{T}E$	NTE RMSE	Cov.	$r\widehat{r}$
Poi	N	100	1	1.641	1.656	0.019	98.3	0.979	0.647	0.662	0.018	94.3	0.690	1.915	1.947	0.035	98.8	0.999
			0	1.268	1.286	0.020	98.0	0.978	0.273	0.291	0.019	94.1	0.485
		500	1	1.644	1.643	0.005	98.9	1.000	0.652	0.656	0.006	94.8	1.000	1.916	1.919	0.006	98.7	1.000
			0	1.264	1.263	0.004	98.6	1.000	0.273	0.276	0.004	94.8	1.000
	B	100	1	1.517	1.504	0.018	98.8	0.959	0.464	0.451	0.018	99.8	0.104	1.813	1.792	0.026	99.3	0.933
			0	1.349	1.341	0.013	97.9	0.946	0.297	0.289	0.011	99.1	0.104
		500	1	1.519	1.512	0.008	99.1	1.000	0.481	0.478	0.006	99.9	0.605	1.823	1.816	0.009	99.7	1.000
			0	1.342	1.339	0.006	99.0	1.000	0.304	0.304	0.004	99.6	0.605
NB	N	100	1	1.513	1.551	0.043	95.0	0.725	0.699	0.724	0.028	95.6	0.508	1.935	2.002	0.070	96.0	0.900
			0	1.236	1.278	0.045	94.5	0.725	0.422	0.451	0.030	94.6	0.508
		500	1	1.511	1.533	0.024	96.2	1.000	0.695	0.701	0.008	93.6	0.992	1.932	1.958	0.028	96.6	1.000
			0	1.238	1.258	0.021	94.8	1.000	0.421	0.425	0.005	92.4	0.992
	B	100	1	1.513	1.554	0.047	96.1	0.547	0.471	0.471	0.013	98.4	0.094	1.804	1.852	0.055	97.6	0.628
			0	1.333	1.382	0.054	95.5	0.532	0.290	0.299	0.012	95.9	0.092
		500	1	1.524	1.519	0.012	96.8	0.994	0.469	0.458	0.013	98.1	0.555	1.821	1.811	0.015	98.5	1.000
			0	1.353	1.354	0.009	96.0	0.996	0.297	0.292	0.006	95.7	0.555
ZIP	N	100	1	1.608	1.667	0.063	99.9	0.544	0.675	0.675	0.014	96.2	0.295	1.920	1.953	0.039	99.9	0.896
			0	1.244	1.278	0.038	99.1	0.581	0.312	0.285	0.028	99.3	0.036
		500	1	1.600	1.591	0.015	99.9	0.996	0.662	0.636	0.027	95.3	0.890	1.908	1.865	0.045	99.6	1.000
			0	1.247	1.229	0.020	98.5	0.996	0.308	0.274	0.034	98.3	0.391
	B	100	1	1.539	1.565	0.037	99.2	0.501	0.510	0.498	0.016	91.4	0.129	1.848	1.879	0.040	99.9	0.688
			0	1.338	1.381	0.048	98.6	0.498	0.309	0.313	0.007	94.0	0.118
		500	1	1.507	1.500	0.015	99.3	0.986	0.497	0.488	0.010	88.9	0.989	1.810	1.814	0.014	99.8	1.000
			0	1.313	1.326	0.017	98.6	0.993	0.303	0.314	0.012	94.3	0.989
ZINB	N	100	1	1.614	1.706	0.099	99.9	0.548	0.525	0.532	0.017	93.1	0.291	1.886	1.958	0.083	99.8	0.786
			0	1.361	1.425	0.072	99.2	0.605	0.272	0.252	0.022	96.8	0.099
		500	1	1.626	1.626	0.032	99.7	0.984	0.538	0.522	0.020	93.3	0.963	1.888	1.880	0.038	99.6	0.993
			0	1.350	1.358	0.027	98.8	0.988	0.263	0.253	0.011	96.6	0.799
	B	100	1	1.603	1.614	0.044	99.1	0.421	0.548	0.537	0.021	95.9	0.130	1.942	1.954	0.049	99.8	0.563
			0	1.394	1.417	0.043	98.8	0.402	0.340	0.340	0.012	97.2	0.140
		500	1	1.535	1.525	0.035	99.3	0.942	0.520	0.524	0.013	96.6	0.883	1.859	1.864	0.040	99.5	0.983
			0	1.339	1.340	0.029	98.9	0.930	0.324	0.339	0.017	96.6	0.878

D’n: distribution; M: mediator; N: sample size; NDE: natural direct effect; NME: natural mediation effect; NTE: natural total effect; RMSE: root mean squared error; Cov: 95% CI coverage; rr: empirical rejection rate of the test; Poi: Poisson, NB: negative binomial; ZIP: zero-inflated Poisson; ZINB: zero-inflated negative binomial; N: normal; B: binary