TABLE 2.

Posterior Medians and 95% Credible Intervals for Variance Components and Relative Risk of COPD Mortality Associated With Cumulative Smoking Proxy Plus Measures of Model Fit

Parameter	Model 1		Model 2		Model 3
(1) Total between-district variance in (log) risk
COPD	Var(ηli)	0.065 (0.063–0.068)	Var(ηli)	0.065 (0.063–0.067)	Var(ηli)	0.065 (0.063–0.067)
Lung cancer	$\mathit{Var}\left(\log \frac{y_{2i}}{e_{2i}}\right)$	0.042	Var(η2i)	0.041 (0.039–0.043)	Var(η2i)	0.041 (0.039–0.043)
(2) Overdispersion variance
COPD	${\sigma }_1^2$	0.0039 (0.001–0.007)	${\sigma }_1^2$	0.0006 (0.0001–0.0023)	${\sigma }_1^2$	0.0006 (0.0001–0.0026)
Lung cancer	—	—	${\sigma }_2^2$	0.0031 (0.0013–0.0049)	${\sigma }_2^2$	0.0031 (0.0013–0.0049)
(3) Between-district  variance  of shared (log) risk	$\mathit{Var}\left(\beta \log \frac{y_{2i}}{e_{2i}}\right)$	0.039 (0.034–0.045)	$\mathit{Var}\left({\beta }^{\ast }{\varphi }_i\right)$	0.054 (0.046–0.063)	$\mathit{Var}\left(\delta {\varphi }_i^{\ast }\right)$	0.061 (0.047–0.069)
(4) Between-district variance of disease-specific residual (log) risk
COPD	Var(ψi)	0.019 (0.016–0.023)	Var(ψli)	0.018 (0.015–0.021)	Var(ψli)	0.0060 (0.0002–0.022)
Lung cancer	—	0	—	0	Var(ψ2i)	0.0065 (0.0002–0.013)
(5) Fraction of total spatial variation shared with other disease
COPD	$\frac{\mathit{Var}\left(\beta \log \frac{y_{2i}}{e_{2i}}\right)}{\mathit{Var}\left(\beta \log \frac{y_{2i}}{e_{2i}}\right)+\mathit{Var}\left({\psi }_{1i}\right)}$	66.9% (61.1%–72.5%)	$\frac{\mathit{Var}\left({\beta }^{\ast }{\varphi }_i\right)}{\mathit{Var}\left({\beta }^{\ast }{\varphi }_i\right)+\mathit{Var}\left({\psi }_{1i}\right)}$	75.0% (70.0%-79.5%)	$\frac{\mathit{Var}\left(\delta {\varphi }_i^{\ast }\right)}{\mathit{Var}\left(\delta {\varphi }_i^{\ast }\right)+\mathit{Var}\left({\psi }_{1i}\right)}$	91.0% (71.4%–99.7%)
Lung cancer	—	100%	—	100%	$\frac{\mathit{Var}\left(\frac{{\varphi }_i^{\ast }}{\delta }\right)}{\mathit{Var}\left(\frac{{\varphi }_i^{\ast }}{\delta }\right)+\mathit{Var}\left({\psi }_{2i}\right)}$	83.9% (70.8%–99.5%)
(6) RR of COPD mortality  associated with unit  increase in smoking  proxya	exp(β)	2.62 (2.44–2.80)	exp(β*)	3.33 (2.94–3.74)	exp(δ2)	3.74 (3.05–4.41)
(7) Deviance		904.3		914.0		913.8
(8) DIC		1775.0		1694.2		1694.4

^aA difference of 1 unit in the value of the smoking proxy between 2 areas can be thought of as equivalent to a difference of 1 in the log relative risk of lung cancer in those 2 areas (see text for further explanation).