Table 3.

Sensitivity analyses for oesophageal cancer incidence among males

	Prior 1	Prior 2	Prior 3	Prior 4	Prior 5	Prior 6
Distribution of SIR
Mean	100.8	99.4	101.5	100.7	100.6	103.6
Standard deviation	10.2	30.8	16.3	14.5	13.5	23.2
Maximum	140.6	455.1	181.2	169.5	166.4	201.8
75% Quartile	107.2	113.1	111.7	110.2	109.4	109.8
Median	96.5	93.5	95.1	95.6	95.9	95.7
25% Quartile	93.3	78.7	89.4	89.9	90.7	90.2
Minimum	87.4	55.9	79.6	79.3	80.0	79.8
90% ratio1	1.3	2.3	1.6	1.5	1.5	1.6
pD2	34.112	138.047	51.305	53.828	53.709	54.098
DIC3	1652.57	1660.32	1650.62	1648.51	1651.02	1650.71
Spatial fraction4	0.56	0.44	0.63	0.48	0.52	0.57
Percent SLAs with Geweke <0.01 for SIR	41.0%	1.9%	3.3%	9.4%	10.3%	10.5%

Notes:

1. The 90% ratio is calculated as the 95^th percentile divided by the 5^th percentile of the smoothed SIR estimates.

2. pD represents the effective number of parameters in the model. Larger values indicate less smoothing of estimates.

3. DIC = Deviance Information Criterion. Smaller values (of at least 5 below) indicate a better model fit.

4. The spatial fraction estimates the relative contribution of spatial and unstructured heterogeneity, and is calculated as: $\text{Spatial}\text{fraction}=\frac{{\theta }_{marginal}^2}{{\theta }_{marginal}^2+{\sigma }^2}$

where ${\theta }_{marginal}^2$ = marginal spatial variance, σ ²= marginal variability of the unstructured random effects between areas. A value close to 1 indicates the spatial heterogeneity dominates, whereas a value close to 0 indicates the unstructured heterogeneity dominates.