The old age effects on cancer incidence are handled and explained differently in the context of the different commonly used carcinogenesis models. For example, the Armitage–Doll model with realistic parameters predicts that cancer incidence should continue to increase roughly as a power of age for ages beyond 80 years. The TSCE and two-stage logistic models predict an asymptotic flattening of the incidence hazard function at old age. This prediction is somewhat at odds with the data mentioned before, which suggest a decrease in cancer incidence at very old ages. Such data are becoming progressively more difficult to ignore, because as more people survive to older ages, the incidence statistics for ages beyond 80 are becoming more accurate and more difficult to explain by poor diagnosis and incomplete adjustment for competing risks.

The mathematical structure of two-stage and multistage cancer models discussed so far precludes them from predicting a decrease in cancer incidence at old ages.75 A new model that explicitly addresses this issue was developed by Pompei and Wilson.83,87,88 The model assumes that carcinogenesis proceeds according to Armitage–Doll multistage principles throughout most of the life span of an individual. At old ages, it is modified by a “cancer extinction” term. An important qualitative implication of the Pompei–Wilson model is that lifetime cancer incidence is predicted to be less than unity, ie, cancer is not a certainty even in the absence of competing risks.

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In general, the lack of detailed treatment of radiation-specific effects typically limits risk predictions from long-term models to exposure conditions where a known shape for the early dose–response relationship, eg, a linear shape, holds. Situations where this dose–response relationship itself requires mechanistic analyses, such as at high fractionated radio-therapeutic doses, are difficult to describe solely with long-term models. Conversely, the more detailed dose responses produced by short-term models can be converted into cancer risk at much later times only by considering the effects of factors such as age at exposure and time since exposure, which are not explicitly taken into account by the short-term formalisms. A unified approach of integrating short- and long-term formalisms is needed, where a detailed initial dose response for premalignant cell numbers is produced over a wide range of doses, and changes to the shape of this dose response over the latency period before the development of cancer are also analyzed. Specific examples of mechanistic models of spontaneous and radiation-induced carcinogenesis unifying short- and long-term processes were developed by Shuryak et al.7,8,37 Alternative examples of unifying long- and short-term models are certainly possible. A summary of the widely accepted short and long-term carcinogenesis models is provided in Table 1.

TABLE 1. A summary of contemporary carcinogenesis models.

Biological model Advantages/disadvantages
Linear–quadratic exponential model Short-term model, simple in formalism
Underestimates risks of high radiation doses
Initiation, inactivation, proliferation model Short-term model, accounts for compensatory proliferation
Armitage–Doll model Long-term model, accounts for background carcinogenesis
Two-stage clonal expansion model Long-term model, fits spontaneous cancer incidence in humans well (to an approximation)
Shuryak–Brenner model Unified approach of integrating short- and long-term formalisms and biological processes


While reported clinical outcomes from following long-term survivors in large epidemiologic studies have provided significant insights and much of the clinical evidence on the impact of radiotherapy for second cancer risks, the application of these findings toward optimizing risks in the modern clinical setting remains controversial and an evolving field of investigation. Genetic markers, molecular pathways, and evolving radiation techniques will serve to more accurately define these risks for subgroups of patients in the emerging era of personalized medicine. There remain many unanswered questions in this field that await further advances in modern genetics and carcinogenesis modeling to address. Future insights and novel tools for optimizing second cancer risks will be invaluable for making treatment decisions to benefit cancer patients.


There are no conflicts of interest to disclose for any of the authors.

John Ng1 and Igor Shuryak2

1Weill Cornell Medical College, New York-Presbyterian Hospital, New York, NY, USA; 2Center for Radiologic Research, Columbia University Medical Center, New York, NY, USA. 


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