Some Mathematical Properties of Cumulative Damage Models Regarding Their Application in Cancer Epidemiology

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Abstract
In an earlier paper, cumulative damage models (CD models) were proposed for modelling the epidemiological aspects of carcinogenesis. In the present paper, further, mainly mathematical support is given for the adequacy of this approach. In the first place, this concerns the aspect that the cumulative damage process is a compound Poisson process. Secondly, it will be demonstrated that the CD models can be considered as a formal generalization of certain well‐known special carcinogenesis models. A more intensive investigation of these models themselves makes it evident that, on account of their mathematical qualities, they will possibly place very efficient new measures at the disposal of epidemiology. A diffusion approximation, however, does, after first experiments, not appear to make the handling of the models any easier but, on the contrary, to lead to a loss of certain pleasant qualities.

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