Table 3.

Selection of random effects using a forward selection procedure

Random effects models	NLMM using NLMIXED			BHM using WinBUGS
	-2logL*	AIC*	BIC*	DIC*	pD
I	91.3	103.3	108.3	104.2	5.6
IIa (εi)	44.5	58.5	64.4	34.8	17.7
IIb (μiA)	67.9	81.9	87.7	67.0	14.5
IIc (νiA)	81.7	95.7	101.5	119.9	10.8
IId (μiB)	64.0	78.0	83.8	65.0	14.6
IIe (νiB)	66.0	80.0	85.8	68.4	8.5
IIIa (εi, μiA)	39.8	55.8	62.4	23.1	15.9
IIIb (εi, νiA)	44.2	60.2	66.9	24.3	17.3
IIIc (εi, μiB)	36.8	52.8	59.4	19.5	24.8
IIId (εi, νiB)	42.6	58.6	65.3	27.3	17.8
IVa (εi, μiB, μiA)	30.6	48.6	56.1	9.9	24.0
IVb (εi, μiB, νiB)	34.9	52.9	60.4	16.1	21.2
IVc (εi, μiB, νiA)	36.5	54.5	62.0	14.8	26.2
IVd (εi, μiB, μiA, ρμBνB)	30.9	50.9	59.2	14.2	24.2
IVe (εi, μiB, νiB, ρμBνB)	34.6	54.6	63.0	22.7	25.9
IVf (εi, μiB, νiA, ρμBνA)	36.7	56.7	65.0	43.9	27.8
Va (εi, μiB, μiA, νiA)	31.0	51.0	59.3	12.1	24.9
Vb (εi, μiB, μiA, νiB)	30.9	50.9	59.2	8.5	23.0

NOTE: A and B correspond to the microsatel-lite instability (MSI) and mutation analysis (MUT) testing, respectively. NLMM = nonlinear mixed effects model; BHM = Bayesian hierarchical model; AIC = Akaike’s information criterion; BIC = Bayesian information criterion; DIC = deviance information criterion; and ρ_D = the effective number of parameters. For the Bayesian analysis, priors for precision parameters of random effects are specified as ${\sigma }_{\epsilon }^{-2}\sim \text{Gamma}(1,1)$ and $({\sigma }_{{\mu }_A}^{-2},{\sigma }_{{\mu }_B}^{-2},{\sigma }_{{\nu }_A}^{-2},{\sigma }_{{\nu }_B}^{-2})\sim \text{Gamma}(2,2)$ · The random effects (ε_i, μ_iA, ν_iA, μ_iB, ν_iB) correspond to study-specific prevalence, MSI sensitivity, MSI specificity, MUT sensitivity, and MUT specificity, respectively.

^*Thirty-three hundred points have been subtracted from -2logL, AIC, BIC, and DIC for presentation. For example, the actual AIC for model I is 3300 + 103.3 = 3,403.3. The bolded cells represent the selected models based on the forward selection procedure.