THE AGE INCIDENCE OF CANCER 



This, however, does not seem to be likely to resemble the 

 actual situation. All or some of the n mutations are going to 

 provide some advantage for selective survival, that is, the 

 numbers of mutants in the population will not remain 

 constant but will form an increasing proportion. Since it is 

 completely unlikely that the advantage of successive muta- 

 tions will be similar at each stage, it is probably impossible 

 to provide a general mathematical expression of the situation. 

 However, we can be certain that if there is this selective ad- 

 vantage, the number of mutations needed to account for 

 a slope of « — I will be proportionately diminished. Instead 

 of 6, it may well need only 2, 3 or 4. In a more recent paper, 

 Armitage and Doll (1957) have considered the case where 

 two sequential mutations are needed and shown that by the 

 use of appropriate constants a reasonably close approxima- 

 tion to the observed mortality can be calculated. They do 

 not, however, claim that this is the only hypothesis which will 

 fit the facts. An interesting point is that relevant to this is the 

 finding that the slope for prostatic cancer is very similar to 

 that for the incidence of prostatic hypertrophy and has a 

 slope of 1 2 to 13 instead of 5 or 6, which is that for cancer 

 generally. There is no faintest possibility that 13 or 14 

 consecutive mutations are needed to induce prostatic 

 malignancy, but there is clear evidence that in some indi- 

 viduals marked proliferation of some prostatic cells is taking 

 place about the critical age. 



The characteristic age incidence of cancer fits naturally 

 into a theory by which a sequence of inheritable changes 

 occurring essentially at random takes place within cell popu- 

 lations. It is very difficult to conceive of any system of 

 reasonable assumption by which a single cause, infection by 

 a virus for example, could give rise to this particular type 

 of age incidence. 



If we accept the view that sequential somatic mutation is 

 the essential basis of cancer, defining mutation as an in- 

 heritable change involving only a small, randomly distributed 



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