Statistical and biological interactions should not be confused

EDITOR—Prescott et al report that smoking increases the risk of myocardial infarction significantly more in women (relative risk 2.24) than in men (relative risk 1.43).1 Interactions between components of smoke and hormonal factors were suspected.

Readers may conclude from this study that men and women do not differ at all. On the basis of data on the prevalence of smoking (table 2 in Prescott et al's paper) and from reported relative risks, we can calculate that in women the risk of developing myocardial infarction during follow up is 5.88% (380/6461) in smokers and 2.63% (132/5011) in non-smokers; in men, the risk is 10.62% (902/8490) in smokers and 7.38% (349/4701) in non-smokers. These are best estimates based on published data; the figures would change slightly if former smokers were removed from the group of non-smokers. The difference that is attributable to smoking was therefore 3.25% in women and 3.24% in men. Over 12 years, smoking caused an additional myocardial infarction in one person out of 31—equally distributed between men and women.

This shows that statistical interaction should not be confused with biological interaction. Statistical interaction concerns the modelling of combined effects of two or more risk factors for a disease in populations, and biological interaction refers to biochemical reactions in an individual. Whether statistical interaction exists or not depends on the specification of the model that is applied to data—“interaction” means that a model that simply adds the effects of two risk factors (in this case sex and smoking) does not accurately describe their joint effect (the risk of myocardial infarction in men who smoke).

Prescott et al used a multiplicative model and found a significant interaction; …