. Author manuscript; available in PMC: 2015 Feb 22.

Published in final edited form as: Biometrics. 2013 May 31;69(2):545–554. doi: 10.1111/biom.12027

Table 2.

Posterior parameter estimates and 95% credible intervals (C.I.) for tooth specific (T), subject specific (S) and population level (P) fixed-effects, variance components, ϕ₁, ϕ₂ and r for the model with subject and tooth nested random effects

	Gaussian		Bridge: Gauss. copula		Bridge: t-copula		GEE
DIC	5283		4157		5490
pD	2578		1931		1692
Brier Score	0.134		0.132		0.134
CV₀, CV₁	0.226, 0.670		0.225, 0.670		0.223, 0.677
Int	−1.61	(−2.54, −0.66)	−1.64	(−2.72, −0.60)	−1.42	(−2.18, −0.58)
T:Age	1.17	(0.76, 1.61)^*	1.48	(0.84, 2.23)^*	1.14	(0.73, 1.59)^*
T:Sex	−1.21	(−2.09, −0.45)^*	−1.89	(−3.65, −0.80)^*	−1.28	(−2.13, −0.60)^*
T:BMI	−0.06	(−0.45, 0.29)	0.06	(−0.35, 0.57)	0.04	(−0.31, 0.39)
T:Smoking	0.38	(−0.08, 0.79)	0.37	(−0.14, 1.08)	0.32	(−0.05, 0.68)
T:HbA1c	0.42	(0.08, 0.88)^*	0.48	(0.05, 0.97)^*	0.39	(0.12, 0.71)^*
T:Molar	4.12	(3.62, 4.75)^*	4.96	(3.68, 7.37)^*	3.78	(3.32, 4.30)^*
S:Age	0.68	(0.43, 0.94)^*	0.64	(0.42, 0.84)^*	0.91	(0.59, 1.21)^*
S:Sex	−0.71	(−1.26, −0.25)^*	−0.80	(−1.26, −0.37)^*	−1.17	(−1.71, −0.65)^*
S:BMI	−0.04	(−0.25, 0.17)	0.02	(−0.17, 0.22)	0.02	(−0.25, 0.29)
S:Smoking	0.23	(−0.04, 0.49)	0.16	(−0.06, 0.48)	0.13	(−0.17, 0.42)
S:HbA1c	0.24	(0.05, 0.50)^*	0.21	(0.02, 0.39)^*	0.34	(0.08, 0.60)^*
S:Molar	2.40	(2.23, 2.57)^*	2.15	(1.97, 2.32)^*	2.78	(2.52, 3.07)^*
P:Age	0.37	(0.22, 0.53)^*	0.46	(0.29, 0.60)^*	0.57	(0.37, 0.76)^*	0.50	(0.33,0.66)^*
P:Sex	−0.39	(−0.71, −0.13)^*	−0.57	(−0.92, −0.27)^*	−0.74	(−1.07, −0.41)^*	−0.52	(−0.92, −0.12)^*
P:BMI	−0.02	(−0.14, 0.10)	0.01	(−0.12, 0.16)	0.01	(−0.16, 0.18)	−0.04	(−0.25, 0.16)
P:Smoking	0.12	(−0.02, 0.28)	0.12	(−0.04, 0.33)	0.08	(−0.11, 0.27)	−0.43	(−0.80, −0.06)^*
P:HbA1c	0.13	(0.03, 0.27)^*	0.15	(0.02, 0.28)^*	0.21	(0.05, 0.38)^*	0.19	(0.04, 0.33)^*
P:Molar	1.31	(1.15, 1.46)^*	1.54	(1.40,1.68)^*	1.76	(1.58, 1.94)^*	1.73	(1.58, 1.88)^*
ϕ₁	0.54	(0.48, 0.61)	0.72	(0.67, 0.76)	0.63	(0.57, 0.69)
ϕ₂	0.58	(0.51, 0.65)	0.45	(0.29, 0.59)	0.63	(0.44, 0.78)
σ₁	5.14	(4.02, 6.72)	4.07	(2.87, 6.17)	3.65	(2.70, 5.13)
σ₂	2.69	(2.26, 3.25)	3.76	(2.49, 5.94)	2.33	(1.46, 3.71)
r	0.15	(0.12, 0.18)	0.15	(0.10, 0.18)	0.15	(0.11, 0.21)

95% C.I. that excludes 0. ϕ₁ controls the distribution of $γ_{i}^{*}$ , while σ₁ is the total subject-specific effect standard deviation given by $s d (γ_{i}^{*}) / ϕ_{2}$ . For the t-copula, there are ν = 2 degrees of freedom.