Applications of Bayesian approach in modelling risk of malaria-related hospital mortality

Table 4 Sensitivity analysis of model M3. Relative changes of fixed effects, deviance information criterion, and variance components for different choices of hyperparameters for $τ_{v}^{2}$ , $τ_{u}^{2}$ and $τ_{h}^{2}$ .

	Hyperparameters for $τ_{v}^{2}$ , $τ_{u}^{2}$ and $τ_{h}^{2}$
	a = 0.5, b = 0.0005	a = 1, b = 0.005	a = 0.001, b = 0.001	a = 0.01, b = 0.01
Model fit
$\bar{D}$	651.54	650.12	652.66	650.06
p _D	59.84	61.01	61.26	61.53
DIC	711.38	711.13	713.92	711.59
Fixed effects
Intercept^§	-2.78 (-4.04, -1.39)	-3.11 (-4.58, -1.69)	-3.15 (-4.88, -1.43)	-3.16 (-4.72, -1.87)
Sex (female)	-0.09 (-0.35, 0.14)	-0.07 (-0.32, 0.18)	-0.08 (-0.34, 0.17)	-0.08 (-0.32, 0.10)
Season (dry)	-0.48 (-0.77, -0.24)	-0.46 (-0.77, -0.14)	-0.45 (-0.74, -0.18)	-0.48 (-0.77, -0.22)
Distance (≤ 5 km)	-5.15 (-7.73, -2.60)	-5.21 (-8.34, -2.49)	-5.19 (-8.36, -2.22)	-5.17 (-10.02, -1.62)
Referral (yes)	4.59 (3.45, 5.88)	4.61 (3.30, 6.37)	4.51 (3.54, 6.48)	4.65 (3.17, 6.65)
Day (weekend)	0.19 (-0.06, 0.38)	0.20 (-0.01, 0.41)	0.20 (-0.03, 0.43)	0.19 (-0.04, 0.40)
Random effects ^†
Areal: structured ( $τ_{v}^{2}$ )	26.27 (10.86, 58.77)	26.58 (12.18, 69.59)	26.44 (8.86, 57.28)	27.34 (11.33, 72.11)
Areal: unstructured ( $τ_{u}^{2}$ )	2.26 (0.003, 9.23)	2.19 (0.008, 2.11)	2.34 (0.008, 6.93)	2.22 (0.008, 2.27)
HF: heterogeneity ( $τ_{h}^{2}$ )	1.21 (0.48, 2.69)	1.24 (0.43, 2.82)	1.23 (0.29, 1.84)	1.24 (0.46, 3.80)

^§Posterior mean and 95% credible intervals are given; HF = Health facility
^†Variance components for the spatially structured effects $τ_{v}^{2}$ , unstructured spatial effects $τ_{u}^{2}$ , and health care random effects $τ_{h}^{2}$

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