Confounding and Simpson's paradox

A common problem when analysing clinical data is that of confounding. This occurs when the association between an exposure and an outcome is investigated but the exposure and outcome are strongly associated with a third variable. An extreme example of this is Simpson's paradox, in which this third factor reverses the effect first observed.1 This phenomenon has long been recognised as a theoretical possibility but few real examples have been presented. Charig et al undertook a historical comparison of success rates in removing kidney stones.2 Open surgery (1972-80) had a success rate of 78% (273/350) while percutaneous nephrolithotomy (1980-5) had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed …