The Age Distribution of Cancer: Implications for Models of Carcinogenesis
1.1. TEN years ago in the introduction to a paper on "Stochastic Models for Carcinogenesis" Armitage and I noted that a variety of models had been put forward, none of which had gained general acceptance, and that no clear body of evidence had been marshalled which would exclude any of them from further consideration (Armitage and Doll, 1961). This was rather discouraging, but it seemed reasonable to maintain an interest in the topic for two reasons. Firstly, many of the concepts on which the models had been based were put forward by research workers on experimental grounds without being formulated in mathematical terms, and it was only sensible to enquire whether these models satisfied the quantitative as well as the qualitative aspects of the data. Secondly, it was possible that the mathematical concepts that were evoked to satisfy the quantitative data might suggest new lines for experimentation. 1.2. In the intervening period, progress has been slow, but the reasons we gave for our interest are still valid and, indeed, have been strengthened. The mechanism by which cancers are produced is still a matter for speculation, but several new possibilities can be considered. Bullough and Lawrence (1960), for example, have obtained evidence of a cybernetic system in which substances are released by cells which act only on cells in the same type of tissue and inhibit their division. In this situation accumulated gene damage might produce a cell that was incapable of reacting to the inhibiting substance (Bullough, 1967). Another possibility was suggested by the discovery that the cells responsible for eliminating foreign proteins might, in some circumstances, react with the body's own cells. Burnet (1967, 1970), therefore, postulates that these immunological reactions fail with increasing age, either because the immunological cells are damaged by mutations or because the total number of divisions, of which they are capable, is limited (Hayflick, 1965). When this happens cellular anomalies, themselves produced by gene mutation, are able to survive and if they have a selective advantage, multiply to produce a cancer. 1.3. During the past ten years many more quantitative data have also become available, relating particularly to the incidence of cancer in man. These data are of two types: cancer registry data recording the incidence of different types of cancer by