Population risk and physiological rate parameters for colon cancer. The union of an explicit model for carcinogenesis with the public health records of the United States.

The relationship between the molecular mechanisms of mutagenesis and the actual processes by which most people get cancer is still poorly understood. One missing link is a physiologically based but quantitative model uniting the processes of mutation, cell growth and turnover. Any useful model must also account for human heterogeneity for inherited traits and environmental experiences. Such a coherent algebraic model for the age-specific incidence of cancer has been developing over the past 50 years. This development has been spurred primarily by the efforts of Nordling [N.O. Nordling, A new theory on the cancer-inducing mechanism, Br. J. Cancer 7 (1953) 68-72], Armitage and Doll [P. Armitage, R. Doll, The age distribution of cancer and a multi-stage theory of carcinogenesis, Br. J. Cancer 8 (1) (1954) 1-12; P. Armitage, R. Doll, A two-stage theory of carcinogenesis in relation to the age distribution of human cancer, Br. J. Cancer 9 (2) (1957) 161-169], and Moolgavkar and Knudson [S.H. Moolgavkar, A.G. Knudson Jr., Mutation and cancer: a model for human carcinogenesis. JNCI 66 (6) (1981) 1037-1052], whose work defined two rate-limiting stages identified with initiation and promotion stages in experimental carcinogenesis. Unfinished in these efforts was an accounting of population heterogeneity and a complete description of growth and genetic change during the growth of adenomas. In an attempt to complete a unified model, we present herein the first means to explicitly compute the essential parameters of the two-stage initiation-promotion model using colon cancer as an example. With public records from the 1930s to the present day, we first calculate the fraction at primary risk for each birth year cohort and note historical changes. We then calculate the product of rates for n initiation-mutations, the product of rates for m promotion-mutations and the average growth rate of the intermediate adenomatous colonies from which colon carcinomas arise. We find that the population fraction at primary risk for colon cancer risk was historically invariant at about 42% for the birth year cohorts from 1860 through 1930. This was true for each of the four cohorts we examined (European- and African-Americans of each gender). Additionally, the data indicate an historical increase in the initiation-mutation rates for the male cohorts and the promotion-mutation rates for the female cohorts. Interestingly, the calculated rates for initiation-mutations are in accord with mutation rates derived from observations of mutations in peripheral blood cells drawn from persons of different ages. Adenoma growth rates differed significantly between genders but were essentially historically invariant. In its present form, the model has also allowed us to calculate the rate of loss of heterozygosity (LOH) or loss of genomic imprinting (LOI) in adenomas to result in the high LOH/LOI fractions in tumors. But it has not allowed us to specify the number of events m required during promotion.