Table 4.

Empirical width and coverage [in brackets] of Wald (W), Chebyshev (C) and exact (E) 95% CIs of the direct effect $\overline{\mathit{DE}}\left({\alpha }_1\right)$, indirect effect $\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$, total effect $\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$ and overall effect $\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$ for simulations under scenario (iv) with m groups, n_i = 1000 individuals per group, and binary outcomes.

		m
		4	6	10	30	100
$\overline{\mathit{DE}}\left({\alpha }_1\right)$	W	0.06[0.94]	0.04[0.96]	0.03[0.97]	0.02[0.97]	0.01[0.97]
	C	0.12[1.00]	0.09[1.00]	0.08[1.00]	0.05[1.00]	0.03[1.00]
	E	6.07[1.00]	4.96[1.00]	3.84[1.00]	2.22[1.00]	1.21[1.00]
$\overline{\mathit{IE}}({\alpha }_1,{\alpha }_0)$	W	0.04[0.80]	0.05[0.87]	0.03[0.90]	0.02[0.94]	0.01[0.94]
	C	0.08[0.95]	0.10[0.99]	0.07[1.00]	0.04[1.00]	0.02[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]
$\overline{\mathit{TE}}({\alpha }_1,{\alpha }_0)$	W	0.04[0.87]	0.04[0.88]	0.03[0.93]	0.02[0.95]	0.01[0.98]
	C	0.09[0.97]	0.10[0.99]	0.06[1.00]	0.04[1.00]	0.02[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]
$\overline{\mathit{OE}}({\alpha }_1,{\alpha }_0)$	W	0.03[0.85]	0.04[0.87]	0.02[0.92]	0.01[0.95]	0.01[0.96]
	C	0.06[0.98]	0.09[1.00]	0.05[1.00]	0.03[1.00]	0.02[1.00]
	E	3.84[1.00]	3.14[1.00]	2.43[1.00]	1.40[1.00]	0.77[1.00]