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.

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Cancer arises through a multistage process, but it is not fully clear how this process influences the age-specific incidence curve. Studies of colorectal and pancreatic cancer using the multistage-clonal-expansion (MSCE) model have identified two phases of the incidence curves. One phase is linear beginning about age of 60, suggesting that at least two rare rate-limiting mutations occur prior to clonal expansion of premalignant cells. A second phase is exponential, seen in earlier-onset cancers occurring before the age of 60 that are associated with premalignant clonal expansion. Here we extend the MSCE model to include clonal expansion of malignant cells, an advance that permits study of the effects of tumor growth and extinction on the incidence of colorectal, gastric, pancreatic and esophageal adenocarcinomas in the digestive tract. After adjusting the age-specific incidence for birth-cohort and calendar-year trends, we found that initiating mutations and premalignant cell kinetics can explain the primary features of the incidence curve. However, we also found that the incidence data of these cancers harbored information on the kinetics of malignant clonal expansion prior to clinical detection, including tumor growth rates and extinction probabilities on three characteristic time scales for tumor progression. Additionally, the data harbored information on the mean sojourn times for prema-lignant clones until occurrence of either the first malignant cell or the first persistent (surviving) malignant clone. Lastly, the data also harbored information on the mean sojourn time of persistent malignant clones to the time of diagnosis. In conclusion, cancer incidence curves can harbor significant information about hidden processes of tumor initiation, premalignant clonal expansion and malignant transformation, and even some limited information on tumor growth before clinical detection.

Several lines of evidence support the premise that screening colonoscopy reduces colorectal cancer (CRC) incidence, but there may be differential benefits for right-and left-sided tumors. To better understand the biological basis of this differential effect, we derived biomathematical models of CRC incidence trends in U.S. and U.K. populations, representing relatively high-and low-prevalence screening, respectively. Using the Surveillance Epidemiology and End Results (SEER) and the Office for National Statistics (ONS) registries (both 1973-2006), we derived stochastic multistage clonal expansion (MSCE) models for right-sided (proximal colon) and left-sided (distal colon and rectal) tumors. The MSCE concept is based on the initiation-promotionprogression paradigm of carcinogenesis and provides a quantitative description of natural tumor development from the initiation of an adenoma (via biallelic tumor suppressor gene inactivation) to the clinical detection of CRC. From 1,228,036 (SEER: 340,582; ONS: 887,454) cases, parameter estimates for models adjusted for calendaryear and birth-cohort effects showed that adenoma initiation rates were higher for right-sided tumors, whereas, paradoxically, adenoma growth rates were higher for left-sided tumors. The net effect was a higher cancer risk in the right colon only after age 70 years. Consistent with this finding, simulations of adenoma development predicted that the relative prevalence for right-versus left-sided tumors increases with increasing age, a differential effect most striking in women. Using a realistic biomathematical description of CRC development for two nationally representative registries, we show age-and sex-dependent biological gradients for right-and leftsided colorectal tumors. These findings argue for an age-, sex-, and site-directed approach to CRC screening.

This study is a comprehensive analysis of the latest follow-up of the Colorado uranium miners cohort using the two-stage clonal expansion model with particular emphasis on effects related to age and exposure. The model provides a framework in which the hazard function for lung cancer mortality incorporates detailed information on exposure to radon and radon progeny from hard rock and uranium mining together with information on cigarette smoking. Even though the effect of smoking on lung cancer risk is explicitly modeled, a significant birth cohort effect is found which shows a linear increase in the baseline lung cancer risk with birth year of the miners in the cohort. The analysis based on the two-stage clonal expansion model suggests that exposure to radon affects both the rate of initiation of intermediate cells in the pathway to cancer and the rate of proliferation of intermediate cells. However, in contrast to the promotional effect of radon, which is highly significant, the effect of radon on the rate of initiation is found to be not significant. The model is also used to study the inverse dose-rate effect. This effect is evident for radon exposures typical for mines but is predicted to be attenuated, and for longer exposures even reversed, for the more protracted and lower radon exposures in homes. The model also predicts the drop in risk with time after exposure ceases. For residential exposures, lung cancer risks are compared with the estimates from the BEIR VI report. While the risk estimates are in agreement with those derived from residential studies, they are about two- to fourfold lower than those reported in the BEIR VI report.

Background The incidence of esophageal adenocarcinoma (EAC) has increased five-fold in the United States since 1975. The aim of our study was to estimate future U.S. EAC incidence and mortality and to shed light on the potential drivers in the disease process that are conduits for the dramatic increase in EAC incidence. Methods A consortium of three research groups calibrated independent mathematical models to clinical and epidemiologic data including EAC incidence from the Surveillance, Epidemiology, and End Results (SEER 9) registry from 1975–2010. We then used a comparative modeling approach to project EAC incidence and mortality to year 2030. Results Importantly, all three models identified birth cohort trends affecting cancer progression as a major driver of the observed increases in EAC incidence and mortality. All models predict that incidence and mortality rates will continue to increase until 2030 but with a plateauing trend for recent male cohorts. The predicted ranges of incidence and mortality rates (cases per 100,000 person years) in 2030 are 8.4–10.1 and 5.4–7.4 respectively for males, and 1.3–1.8 and 0.9–1.2 for females. Estimates of cumulative cause-specific EAC deaths among both sexes for years 2011–2030 range between 142,300 and 186,298, almost double the number of deaths in the past 20 years. Conclusions Through comparative modeling, the projected increases in EAC cases and deaths represent a critical public health concern that warrants attention from cancer control planners to prepare potential interventions. Impact Quantifying this burden of disease will aid health policy makers to plan appropriate cancer control measures.