We use general multistage models to fit the age-specific incidence of colorectal cancers in the Surveillance, Epidemiology, and End Results registry, which covers Ϸ10% of the U.S. population, while simultaneously adjusting for birth cohort and calendar year effects. The incidence of colorectal cancers in the Surveillance, Epidemiology, and End Results registry is most consistent with a model positing two rare events followed by a high-frequency event in the conversion of a normal stem cell into an initiated cell that expands clonally to give rise to an adenomatous polyp. Only one more rare event appears to be necessary for malignant transformation. The two rare events involved in initiation are interpreted to represent the homozygous loss of adenomatous polyposis coli gene function. The subsequent transition of a preinitiated stem cell into an initiated cell capable of clonal expansion via symmetric division is predicted to occur with a frequency too high for a mutational event but may reflect a positional effect in colonic crypts. Our results suggest it is not necessary to invoke genomic instability to explain colorectal cancer incidence rates in human populations. Temporal trends in the incidence of colon cancer appear to be dominated by calendar year effects. The model also predicts that interventions, such as administration of nonsteroidal anti-inflammatory drugs, designed to decrease the growth rate of adenomatous polyps, are very efficient at lowering colon cancer risk substantially, even when begun later in life. By contrast, interventions that decrease the rate of mutations at the adenomatous polyposis coli locus are much less effective in reducing the risk of colon cancer.T he first attempts to formulate a quantitative description of carcinogenesis reflecting essential biological processes on the pathway from a normal cell to a cancer cell go back almost half a century (1). Perhaps the best known model is due to Armitage and Doll (2), who noticed that the age-specific incidence of many carcinomas appeared to increase approximately with power of age, which could be related to the number of rate-limiting steps involved in the formation of a malignant tumor. However, it was also realized that a two-stage model with clonal expansion of intermediate cell populations could generate similar age-specific incidence curves (3). These considerations, combined with the idea of recessive oncogenesis first formulated by Knudson (4), led to the two-stage clonal expansion (TSCE) model, which explicitly incorporates clonal expansion as a stochastic process during carcinogenesis (5-7).Recent studies of the genetic profiles of various tumors suggest the involvement of several genes during tumorigenesis. A case in point is colorectal cancer, perhaps the best studied cancer in terms of the putative sequence of genetic events in its pathogenesis (8-12). Over the past 10 years, an impressive number of studies have been carried out identifying several molecular pathways involved in the development of colorectal cancer (see ref...

The observation that the age-specific incidence curve of many carcinomas is approximately linear on a double logarithmic plot has led to much speculation regarding the number and nature of the critical events involved in carcinogenesis. By a consideration of colorectal and pancreatic cancers in the Surveillance Epidemiology and End Results (SEER) registry we show that the log-log model provides a poor description of the data, and that a much better description is provided by a multistage model that predicts two basic phases in the age-specific incidence curves, a first exponential phase until the age of ≈60 followed by a linear phase after that age. These two phases in the incidence curve reflect two phases in the process of carcinogenesis. Paradoxically, the early-exponential phase reflects events between the formation (initiation) of premalignant clones in a tissue and the clinical detection of a malignant tumor, whereas the linear phase reflects events leading to initiated cells that give rise to premalignant lesions because of abrogated growth/differentiation control. This model is consistent with Knudson's idea that renewal tissue, such as the colon, is converted into growing tissue before malignant transformation. The linear phase of the age-specific incidence curve represents this conversion, which is the result of recessive inactivation of a gatekeeper gene, such as the APC gene in the colon and the CDKN2A gene in the pancreas.colorectal | pancreatic | multistage carcinogenesis | neoplastic progression | Knudson's "two-hit" hypothesis T he precise shape of the age-specific incidence of various cancers, especially of nonembryonal solid tumors, and what information can be gleaned from their behavior, is still subject to scientific debate. A widely held view, put forward independently by Muller (1) and Nordling (2) and which reflects the basis of the Armitage-Doll model (3), conceives the stepwise progression of normal cells to cancer as a multistage process involving a number of rate-limiting (epi)genetic events. When viewed at the population level, this assumption uniquely defines the mathematical shape of the age-specific incidence of a cancer, also reflecting the assumed number of rate-limiting events. Indeed, at some level of mathematical approximation (see, e.g., ref. 4), the sequential nature of such a multistep process imposes a power-law behavior, that is, the age-specific incidence of cancers that arise as a consequence of several rate-limiting genomic alterations is predicted to increase with a power of age that is one less than the number of events necessary for malignant transformation. Although it is generally recognized that the carcinogenic process is more complicated and possibly punctuated by selection of advantageous mutations and clonal expansions (5), the qualitative power-law behavior of the age-specific cancer incidence is still considered a reasonable approximation for many cancers and continues to be invoked to argue for or against the importance of specific biological events in car...

A two-mutation model for carcinogenesis is reviewed. General principles in fitting the model to epidemiologic and experimental data are discussed, and some examples are given. A general solution to the model with time-dependent parameters is developed, and its use is illustrated by application to data from an experiment in which rats exposed to radon developed lung tumors.