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Using The Negative Exponential Model To Describe Changes In Risk Of Smoking-Related Diseases Following Changes In Exposure To Tobacco

Peter N. Lee, John Hamling, John Fry, Barbara Forey

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Recently published analyses for four smoking-related diseases show that the declining excess relative risk by time quit is well fitted by the negative exponential model. These analyses estimated the half-life of this excess, that is, the time after quitting when the excess relative risk reaches half that for continuing smokers. We describe extensions of the simple model. One quantifies the decline following an exposure reduction. We show that this extension satisfactorily predicts results from studies investigating the effect of reducing cigarette consumption. It may also be relevant to exposure reductions following product-switching. Another extension predicts changes in excess relative risk occurring following multiple exposure changes over time. Suitable published epidemiological data are unavailable to test this, and we recommend its validity to be investigated using large studies with data recorded on smoking habits at multiple time points in life. The basic formulae described assume that the excess relative risk for a continuing smoker is linearly related to exposure and that the half-life is invariant of age. We describe model adaptations to allow for nonlinear dose-response and for age-dependence of the half-life. The negative exponential model, though relatively simple, appears to have many potential uses in epidemiological research for summarizing variations in risk with exposure changes.