Age-specific incidence of cancer: Phases, transitions, and biological implications

Abstract

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 approximately 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.

Fig. 1.

Multistage clonal expansion (MSCE) model. Pictorial representation of the MSCE model. Cells arrive in the first preinitiation stage according to a Poisson process with intensity μ₀X, where X is the number of normal susceptible cells. A cell in the ith preinitiation stage can divide into one ith preinitiated cell and one (i + 1)th preinitiated cell with rate μ_i, for i = 1,…,k − 3. A (k − 2)th preinitiated cell can divide into one (k − 2)th preinitiated cell and one initiated cell with rate μ_{k − 2}. Once a cell is initiated, it expands clonally via a birth–death–mutation process with rates α,β,μ_{k − 1}, respectively.

Fig. 2.

Colorectal cancer incidence. (Upper) SEER CRC incidence. (Lower) CRC incidence adjusted for secular trends (using estimated calendar year and birth-cohort effects from the three-stage model fit). Solid line: three-stage hazard. The slope of the linear phase of the hazard and the mean sojourn time of premalignant lesions can be determined directly from the adjusted incidence data.

Fig. 3.

Pancreatic cancer incidence. (Upper) SEER PC incidence. (Lower) PC incidence adjusted for secular trends (using estimated calendar year and birth-cohort effects from the three-stage model fit). Solid line: three-stage hazard. The slope of the linear phase of the hazard and the mean sojourn time of premalignant lesions can be determined directly from the adjusted incidence data.