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

The existence of a dose-related increase of lung cancer risk in cigarette smokers has been indisputably established. This finding, however, is not confirmed at low doses (< 5 cigarettes/day), there still being a lack of epidemiological data. The use of mathematical models of carcinogenesis to extrapolate from higher doses allows estimation of the risk for very light smokers. The present study has been designed to compare a set of mathematical models, i.e. one-hit, two-stage, multi-stage, logit, probit, and Weibull, in extrapolating relative risks at low doses from the data of nine large cohort studies on cigarette smokers reported in the IARC Scientific Monograph on tobacco smoking. All models evaluated, apart from the one-hit, achieved a good fit, with the proportion of explained variance ranging between 61% and 67%. The relative risk estimates for passive smokers from the most updated epidemiological studies were taken into account to evaluate, on the basis of these models, the corresponding exposure in terms of 'cigarette equivalent' smoked. These values ranged from 0.21 to 0.43 cigarettes/day for the two-stage and multi-stage model, while probit, logit and Weibull models, yielded estimates one or even two orders of magnitude lower. The authors emphasize the substantial agreement between the estimates of 'cigarette equivalent' based on the application of two-stage and multi-stage models to the epidemiological evidence on the effect of passive smoking and to the data based on the comparison of tobacco metabolites in active and passive smokers.