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Table 2 Example of non-comparability of SMRs

From: Direct risk standardisation: a new method for comparing casemix adjusted event rates using complex models

Casemix group National standard death rate Hospital A: Death rate Hospital A: Casemix proportions Hospital B: Death rate Hospital B: Casemix proportions
1. High risk 0.9 0.8 0.4 0.8 0.3
2. Low risk 0.1 0.2 0.6 0.2 0.7
SMR    O = (0.4×0.8) + (0.6×0.2)   O = (0.3×0.8) + (0.7×0.2)
    E = (0.4×0.9) + (0.6×0.1)   E = (0.3×0.9) + (0.7×0.1)
    SMR = 105   SMR = 112