Table 2

Illustration of Simpson's paradox using the standardised mortality ratio (SMR) for two surgeons with the same observed risk-specific 30-day mortality

Surgeon ASurgeon B
Low-risk patientsN=100N=50
Deaths (n)10 (10%)5 (10%)
Number expected10 (10%)5 (10%)
High-risk patientsN=50N=100
Deaths (n)15 (30%)30 (30%)
Number expected10 (20%)20 (20%)
All patientsN=150N=150
Deaths (n)2535
Number expected2025
  • 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.