Illustration of Simpson's paradox using the standardised mortality ratio (SMR) for two surgeons with the same observed risk-specific 30-day mortality
| Surgeon A | Surgeon B | |
|---|---|---|
| Low-risk patients | N=100 | N=50 |
| Deaths (n) | 10 (10%) | 5 (10%) |
| Number expected | 10 (10%) | 5 (10%) |
| High-risk patients | N=50 | N=100 |
| Deaths (n) | 15 (30%) | 30 (30%) |
| Number expected | 10 (20%) | 20 (20%) |
| All patients | N=150 | N=150 |
| Deaths (n) | 25 | 35 |
| Number expected | 20 | 25 |
| SMR | 1.25 | 1.40 |
Example taken from Reference 12, the companion research article for this editorial. The two surgeons have identical observed and expected mortality rates for low-risk and high-risk patients. Their performance for low-risk patients is as expected—the number of observed deaths equals the expected number. Their performance for high-risk patients is worse than expected, but to the same extent. Both surgeons have the same 1.5-fold elevation in deaths for high-risk patients. Yet, the overall SMR of Surgeon A is substantially lower (ie, better) than that of Surgeon B.