Estimating the benefits of cholesterol lowering: are risk factors for coronary heart disease multiplicative?

It is often stated that the major risk factors for coronary heart disease (CHD)--smoking, high blood pressure and high serum cholesterol--are not merely additive but act together such that each multiplies the effects of the others. Economic analyses in which the benefits of risk factor modification are estimated often reflect this. This paper explains how predictive models based on the simplest form of the multiple logistic function inevitably predict greater benefit from cholesterol lowering in those in whom other risk factors are adverse; this results from the model itself, rather than the data. CHD death rates from the screenee population of the Multiple Risk Factor Intervention Trial are examined: these suggest that the relationship between cholesterol and both other major risk factors is closer to additive than to multiplicative. When the benefits of cholesterol lowering are estimated, a model based on additive risk, specifying product ("interaction") terms, is to be preferred.