Mathematical modelling in risk/exposure assessment of tobacco related lung cancer

The existence of a dose-related increase of lung cancer riskin cigarette smokers has been indisputably established. Thisfinding, however, is not confirmed at low doses (< 5 cigarettes/day),there still being a lack of epidemiological data. The use ofmathematical models of carcinogenesis to extrapolate from higherdoses allows estimation of the risk for very light smokers.The present study has been designed to compare a set of mathematicalmodels, i.e. one-hit, two-stage, multi-stage, logit, probit,and Weibull, in extrapolating relative risks at low doses fromthe data of nine large cohort studies on cigarette smokers reportedin the IARC Scientific Monograph on tobacco smoking. All modelsevaluated, apart from the one-hit, achieved a good fit, withthe proportion of explained variance ranging between 61% and67%. The relative risk estimates for passive smokers from themost updated epidemiological studies were taken into accountto evaluate, on the basis of these models, the correspondingexposure in terms of ‘cigarette equivalent’ smoked.These values ranged from 0.21 to 0.43 cigarettes/day for thetwo-stage and multistage model, while probit, logit and Weibullmodels, yielded estimates one or even two orders of magnitudelower. The authors emphasize the substantial agreement betweenthe estimates of ‘cigarette equivalent9 based on the applicationof two-stage and multi-stage models to the epidemiological evidenceon the effect of passive smoking and to the data based on thecomparison of tobacco metabolites in active and passive smokers.