Mutation, cell kinetics, and subpopulations at risk for colon cancer in the United States.

We have extended the algebraic models for cancer initiation and progression developed by Nordling, Armitage-Doll and Knudson-Moolgavkar to include the effect of cell turnover rate in normal tissue, stochastic growth of preneoplastic adenomas, and the general case wherein a subfraction of the population is at risk. We have also gathered the mortality data available for the United States from 1900 to 1991 and categorically organized them by birth year cohorts and age specific death rates for ages 0 to 104 in 5-year groupings. Using these data, we first explored the quantitative nature of the biases of underreporting or misdiagnosis as historical age-dependent functions. Then we used the extended algebraic model to calculate the parameters of subpopulation fraction at risk, mutation rates and adenoma growth rates. We observe that death rates for all cancers are low in childhood and early adulthood, rise in middle age in an approximately linear manner, reach a maximum in old age, and even after correction for reporting bias, decrease markedly in extreme old age. We represent this behavior as the natural result of a continuous process of cell division, death and mutation within a subpopulation at risk. This population at risk within any birth cohort is defined by the product of a constant inherited risk factor multiplied by a historically valuable environmental risk factor. Our formulation permits explicit calculation of the fraction at risk of death from any cancer as a historical function. With regard to the algebraic description of the process of carcinogenesis, we use Nordling's concept that n genetic events in a cell population of constant cell number are required to initiate a colony capable of net cell growth or 'adenoma.' We adopt and extend Moolgavkar's use of the 'Gambler's Ruin' stochastic process to describe the probability of adenoma survival and the canonical expectation that a surviving adenoma will soon contain many initiated cells by virtue of stochastic distribution of surviving cells. We consider that within the growing adenoma, it is necessary for a cell to acquire m additional mutations in order to attain the carcinoma phenotype of cell growth rapid enough to kill in a short time. This would be irrespective of the need for any additional genetic events that may define the subsequent phenotypes of large lethal tumors, as these would be automatically acquired and be physiologically selected in any rapidly growing cell mass. It is evident that the steps of initiation and progression are dependent on both the rates of genetic change per cell division and the cell kinetic rates of division and death. We have chosen to first examine colon cancer because the rates of cell division in normal colonic epithelium, dysplastic adenomas and small carcinomas have been directly observed as reported herein. For colon cancer, we calculate that about 65% of the US population is at risk for both males and females, and that this fraction has been constant for the earliest recorded birth cohorts of the mid-19th century to the beginning of the 20th century. The changes that have been observed in colon cancer mortality rates appear to arise from historical changes in death rates by unknown 'other causes of death', which share both genetic and environmental risk factors with colon cancer and explicitly include undiagnosed deaths by colon cancer. Considering all possible values of n and m, we find the case of n=2 and m=1 to give the best concordance with present knowledge of mutations in the colon by the loss of two alleles of the APC gene and the observation that for m=1, a rate of genetic change approximately equal to that calculated for initiation mutation rates is obtained. Our estimates for the rate of initiation and progression mutation rates show no significant historical shifts and are approximately 1-2x10-7 events per cell division. (ABSTRACT TRUNCATED)