Authors’ response: Understanding variation in disease risk

that neither the exact nor the approximate solution describes cancer incidence data well, and that models incorporating cell proliferation kinetics do better. 4 Be that as it may, for any stochastic model, stochastic heterogeneity is immediately introduced if the stochastic solution is used. Inter-individual variations in susceptibility arising from variations in the rates of critical biological processes can be modelled by assuming a distribution on the parameters of the model. Major gene defects, such as FAP, can be modelled along the lines suggested by Knudson 10 for retinoblastoma by assuming that one of the mutations along the pathway to carcinogenesis has been inherited by every cell in the tissue of interest. The critical point here is that all sources of inter-individual variation in susceptibility can be modelled using specific biological considerations. It is not necessary to use the artifice of multiplying the hazard function of the Weibull model by a frailty parameter, as Aalen et al. suggest. 1 I agree with the authors that ignoring heterogeneity and frailty can yield misleading inferences. That said, another equally important factor in the misinterpretation of epidemiological data is the ubiquitous and often inappropriate application of the proportional hazards model for analysis and the virtually universal use of the relative risk as a measure of effect. It is becoming increasingly clear that summary measures of exposure, such as cumulative exposure, cannot capture the impact of complex temporal patterns of exposure on disease risk, 5,6 and that the relative hazard, which is the target of estimation with the proportional hazards model, has serious limitations. 7,8 For cohort data, the use of parametric hazard functions derived from multistage models of carcinogenesis that explicitly incorporate patterns of exposure can simultaneously address both issues and provide insights that are difficult or impossible to obtain using the proportional hazards model. Invited commentary: is it time to retire the " pack-years " variable? Maybe not! Luebeck G et al. Diesel engine exhaust and lung cancer mortality: Time-related factors in exposure and risk. which permits non-commercial reproduction and distribution of the work, in any medium, provided the original work is not altered or transformed in any way, and that the work properly cited. For commercial re-use, please contact [email protected]