Cumulative damage models in cancer epidemiology: application to human incidence and mortality data

Cumulative damage models are a special class of mathematical models within reliability theory that describe the probability of failure of a given system under the impact of a damaging environment. Though originally introduced to handle wear and tear processes, their concepts can easily be interpreted in terms of the epidemiologic aspects of human carcinogenesis. This paper introduces the new approach and demonstrates its applicability to human cancer incidence and mortality data from Denmark and the Federal Republic of Germany. A slight simplification of the originally stochastic model provides an explicit formula for the relative risk between different populations, which predicts that this basic measure used in cancer epidemiology may have to be considered age-dependent in contrast to a widely used practice which, for convenience, postulates age-independent relative risks. A comparison with empirical data reveals that the concept of age-dependent relative risks is not inconsistent with real world examples of cancer incidence. Thus, some basic assumptions and concepts of epidemiology concerning carcinogenesis and strategies for data analysis may require reconsideration.