Significance test for differences in standard mortality ratios



The table below gives a hypothetical example for standard mortality
ratios (SMR) with their 95% Poisson lower (LCL) and upper (UCL)
confidence limits for the number (obs) of deaths in three different
populations (A,B,C) and the expected number (exp) in their respective
appropriate reference population.

What is the exact test for the null that SMR-B = SMR_A and SMR-C =
SMR-A ?

Asymptotically I would use the (scaled) variances s^2 = obs, but I
would prefer an exact test.


Popl. | obs/ exp : ( LCL, SMR, UCL )
A | 55/ 75.34: (0.5500,0.7300,0.9502)
B | 44/ 81.73: (0.3912,0.5384,0.7227)
C | 33/ 61.28: (0.3707,0.5385,0.7563)

Many thanks in advance, Rainer Facius

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