. Author manuscript; available in PMC: 2014 Nov 6.

Published in final edited form as: Stat Med. 2013 May 6;32(24):4211–4228. doi: 10.1002/sim.5830

Table 5.

Estimated causal effects (and 95% bootstrap percentile CIs) based on the mediation formula approach with ‘exact’ integration and Monte Carlo integration in a three-mediator model using dental data.

		Mediation Formula
		‘Exact’ Integration	Monte Carlo Integration^#
Sealant (binary), AvgOHI (continuous), and Visit (binary)	Total TE	0.18 (0.03, 0.34)	0.18 (0.03, 0.34)
	Direct DE	0.13 (−0.03, 0.29)	0.13 (−0.03, 0.29)
	Indirect IE	0.05 (0.00^$, 0.11)	0.05 (0.00, 0.11)
	Through Sealant (IE₁)^*	0.00 (−0.02, 0.02)	0.00 (−0.02, 0.02)
	Through AvgOHI and Visit (IE₂₃)^*	0.05 (0.01, 0.11)	0.05 (0.01, 0.11)
	Through AvgOHI (IE₂)^*	0.04 (0.00, 0.08)	0.04 (0.00, 0.08)
	Through Sealant and Visit (IE₁₃)^*	0.02 (−0.02, 0.05)	0.02 (−0.02, 0.05)
	Through Visit (IE₃)^*	0.02 (−0.01, 0.05)	0.02 (−0.01, 0.05)
	Through Sealant and AvgOHI (IE₁₂)^*	0.04 (−0.00, 0.08)	0.04 (−0.00^$, 0.08)

Monte Carlo integration with 1,000,000 samples was used for estimation of causal effects.

Assumes correlation between $M_{i}^{(*)} (t_{i}), M_{j}^{(*)} (t_{j}) (i, j = 1, 2, 3 and i \neq j)$ is constant over all t_i and t_j.

‘0.00’ indicates a positive value, and ‘−0.00’ a negative value, less than 0.005 in absolute value.