Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Table 5 Estimated area-level random effects from Bayesian spatial survival models

		Area random-effects (95% CrI)
Model	Description¹	Spatial (*spat_σ*²_u)²	Unstructured (*spat_σ*²_v)³	Total (*spat_σ*²)⁴	Spatial fraction⁵(95% CrI)
7	Null (no covariates) only area random effects: spat_u_j & spat_v_j	0.018 (0.016, 0.23)	0.006 (0.004, 0.012)	0.024 (0.012, 0.28)	0.70 (0.51, 0.82)
8	Individual covariates	0.010 (0.005, 0.018)	0.005 (0.002, 0.011)	0.015 (0.009, 0.024)	0.64 (0.38, 0.86)
9	Individual covariates & area remoteness	0.007 (0.003, 0.015)	0.005 (0.002, 0.010)	0.012 (0.006, 0.021)	0.56 (0.26, 0.82)
10	Individual covariates & area disadvantage	0.006 (0.003, 0.13)	0.005 (0.002, 0.011)	0.011 (0.007, 0.019)	0.58 (0.29, 0.81)
11	Full model: all individual & area covariates	0.006 (0.002, 0.013)	0.005 (0.003, 0.009)	0.011 (0.006, 0.019)	0.55 (0.35, 0.73)
12	All covariates with no spatial effect (spat_u _j excluded)	-	0.009 (0.003, 0.013)
13	All covariates with no unstructured effect (spat_v _j excluded)	0.009 (0.003, 0.014)	-

CrI: Credible Interval.
1. Models 8 to13 adjusted for all individual-level covariates; Model 9 also adjusted for area remoteness; Model 10 also adjusted for area disadvantage, Model 11 also adjusted for area remoteness and area disadvantage. Models 12 and 13 are adjusted for all covariates in Model 11 but exclude the spatial and unstructured random effects respectively.
2. Spatial variance (spat_σ²_u).
3. Unstructured variance (spat_σ²_v).
4. Total variance ( $spat_σ^{2} = spat_σ_{u (m)}^{2} + spat_σ_{v}^{2}$ ).
5. Refer to Appendix 2 for details.

ISSN: 1476-072X