Bayesian versus frequentist statistical inference for investigating a one-off cancer cluster reported to a health department

Table 2 Frequentist confidence intervals and p-values adjusted for silent multiple comparisons, Illawarra and Brisbane ABC cancer clusters

	Illawarra, leukaemia observed = 12, expected = 3.49 SIR = 3.44	Brisbane, ABC, breast cancer observed = 10, expected = 1.6 SIR = 6.25
Number of comparisons	Confidence interval (p-value)	Confidence interval (p-value)
1	1.78, 6.01 (0.00056)	3.00, 11.49 (0.000014)
10	1.30, 7.27 (0.0056)	2.11, 14.10 (0.00014)
100	0.99, 8.40 (0.0548)	1.55, 16.44 (0.0014)
500	0.83, 9.13 (0.2456)	1.27, 17.98 (0.0071)
1000	0.77, 9.44 (0.4309)	1.16, 18.62 (0.0142)
5000	0.65, 10.14 (0.9403)	0.96, 20.08 (0.0689)
10000	0.61, 10.43 (0.9964)	0.89, 20.69 (0.1331)
40000	0.53, 11.0 (>0.9999)	0.76, 21.90 (0.4353)
50000	0.52, 11.1 (>0.9999)	0.74, 22.09 (0.5104)

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