Letters

Confounding and Simpson's paradox

EDITOR,--Steven A Julious and Mark A Mullee discuss confounding and Simpson's paradox, defining confounding as occurring "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 In their analysis of my and colleagues' article on treatments for surgery to remove kidney stones the authors correctly observe that the size of the stones is the single most important factor in determining the success of treatment. The fact that the figures show that open stone surgery has a higher success rate for both small and large stones but that the overall success rate is greater with percutaneous nephrolithomy is a paradox. This probably reflects the numbers in each group.

The authors' deduction that factors such as the patient's age and characteristics determine treatment does not, however, hold for a historical perspective, when all patients were treated consecutively with the only treatment available at this time. There is no reason to believe that patients treated 10 or 15 years ago had any different characteristics from those of patients presenting for modern day treatments.

The authors' argument that randomised trials are necessary to show any effect of treatment is difficult to accept when you have a new form of treatment that is so clearly superior to all previous forms of treatment that to compare one against the other--that is, open surgery versus lithotripsy--for a small stone would be unethical with regard to morbidity.

The main aim of the paper was not really to compare success rates but more to show that, when success rates were comparable, morbidity and cost to the health service were much reduced. I therefore do not see what purpose could be served by producing a model to include multiple regression or multiple logistic regression in analysing the variance as it would only confound the clinicians.

Consultant urologist Epsom General Hospital, Epsom, Surrey KT18 7SG

C R Charig 

1. Julious SA, Mullee MA. Confounding and Simpson's paradox. BMJ 1994;309:1480-1. (3 December.) [Free Full Text]