CARCINOGENESIS AS THE RESULT OF TWO 

 INDEPENDENT RARE EVENTS 



E. H. MOLE 

 31.R.C. Radiobiological Research Unit, Harivell, England 



SUMMARY 



The human evidence on the increase in cancer incidence in survivors of the atom 

 bomb explosion at Hiroshima (which varies with the age of the individual at the time of 

 exposure) and the animal evidence relating quantity of bone-seeking isotope and bone- 

 cancer incidence are both compatible with the general hypotheses that cancer arises as 

 a result of two mdependent rare events. 



The intention of this note is not to report new results but to illustrate a new 

 way of looking at old results. The basic ideas of Armitage and Doll (1957) 

 already adumbrated (pp. 13,15) can provide a common explanation of two 



0-01 0-05 0-1 



1000 



5000 

 10,000 



0-5 1-0 5 10 50 



Injected dose (//c/kg) 



Fig. 1. Incidence of bone tumours in CAF^ mice given single injections of different bone- 

 seeking isotopes (data of Finkel and her colleagues as plotted by Lamerton, 1958). The dashed 

 curve gives the shape of the theoretical incidence curve if bone-tumour production was 

 proportional to the square of the injected dose, Mfe-shortening and excretion of the dose being 

 disregarded (cf. Mole, 1962). 



apparently unrelated phenomena, (a) the markedly curvilinear dose-response 

 in experiments on bone carcinogenesis by a variety of bone-seeking isotopes in 

 the mouse (Fmkel, 1959; Fig. 1) and in the dog (Dougherty, 1962), and (6) the 

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