Estimating the potential disease rate reduction under varying conditions of combined effects

The disease rate difference between people exposed and not exposed to some factor is the familiar estimate of attributable risk. When there are two or more causal exposures which demonstrate joint effects and are independently distributed, partitioning a population's overall rate between factors requires estimates of the marginal distributions of exposures and the independent (unconditional) and combined rate ratios for each exposure factor. The net potential reduction in the overall disease rate resulting from elimination of one of the exposures depends on these parameters and on the model of combined effect assumed, additive, multiplicative or some departure therefrom. In this paper the authors illustrate the extent to which the assumed model of combined effect of exposures determines which parameters need to be specified to estimate disease rate reductions. The concepts presented are demonstrated algebraically and with simulated hypothetical data. An application of the method is given with data from a case-control study of smoking, asbestos exposure and lung cancer.