Epidemiologists, for reasons that are primarily historical and mathematical, have instead preferred a model for statistical independence that is based on additivity on a logarithmic scale applied to risk, rather than 1 minus risk. The multiplicative model for independence specifies that: Pr[D|A,B]Pr[D|A¯,B¯] = Pr[D|A,B¯]Pr[D|A¯,B¯]Pr[D|A¯,B]Pr[D|A¯,B¯], i.e. the relative risk associated with the combined exposure is the product of the two relative risks. Another way to think of this is that the relative risk for A relative to nonA (or B relative to nonB) is the same across levels of B (or A). If the disease is rare in the population under study, then the above model is approximately equivalent to a multiplicative model for the odds ratios, which becomes additivity on the logistic scale. In an unfortunate use of terminology, epidemiologists refer to departures from this model as effect modification, a jargon that strongly implies that one factor modifies the effect of the other. (A recent advance is instead to use the phrase effect-measure modification [3].)
