Multistage Models of Carcinogenesis

Armitage, P.

doi:10.2307/3430046

Cited by 10 publications

(9 citation statements)

References 12 publications

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“…For large N, this simplifies to G(t)=1-e -NF(t) , which is accurate to 10 -10 for N=10 8 cells. As discussed by both Moolgavkar (1978) and Armitage (1985), the age-specific incidence function for the organ tissue is not the density function G'(t) itself, but the associated hazard function, given by h c (t)=G'(t)/[1-G(t)], which represents the incremental risk of cancer per unit time given that the tissue has been cancer-free to time t. Completing the derivation, h c (t)=e -NF(t) Nf(t)/ e -NF(t) = Nf(t). We note that the age-specific cancer incidence for a site tissue is related to the probability density function for one cell by the constant N, thus leaving the Beta model as f(t)=αt k-1 (1-βt), modified by only by a constant (absorbed into α) to apply to a multicellular organ site.…”

Section: Appendixmentioning

confidence: 92%

Age Distribution of Cancer: The Incidence Turnover at Old Age

Pompei

Wilson

2001

Human and Ecological Risk Assessment: An International Journal

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In recent years data on cancer incidence in the USA, the Netherlands, and in Hong Kong indicate a flattening and perhaps a turnover at advanced age, but no model has been successful in fitting this data and thus providing clues to the underlying biology. In this work we assume these data are reliable and free from bias. We find that a Beta distribution fits SEER age-specific cancer incidence data for all adult cancers extremely well, and its interpretation as a model leads to the possibility that there is a beneficial cancer extinction process that becomes important at elevated age. Particularly evident from the data is the apparent remarkable uniformity of adult cancers peaking in incidence at about the same age, including cancers in other countries. Possible biological mechanisms include increasing apoptosis and cell senescence with age. Further, the model suggests that cancer is not inevitable at advanced age, but reaches a maximum cumulative probability of affliction with any cancer of about 70% for men and 53% for women in the US, and much smaller values for individual cancers.

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Section: Appendixmentioning

confidence: 92%

Age Distribution of Cancer: The Incidence Turnover at Old Age

Pompei

Wilson

2001

Human and Ecological Risk Assessment: An International Journal

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“…Cancer initiation, promotion, and progression involve a series of epigenetic and genetic alterations affecting oncogenes and tumor suppressor genes [1][2][3][4]. Inhibition of each stage of carcinogenesis has been shown to be achievable by administering chemical agents.…”

Section: Introductionmentioning

confidence: 99%

Phytochemicals: cancer chemoprevention and suppression of tumor onset and metastasis

Shu

Cheung

Khor

et al. 2010

Cancer Metastasis Rev

218

153

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Carcinogenesis is a multi-step process which could be prevented by phytochemicals. Phytochemicals from dietary plants and other plant sources such as herbs are becoming increasingly important sources of anticancer drugs or compounds for cancer chemoprevention or adjuvant chemotherapy. Phytochemicals can prevent cancer initiation, promotion, and progression by exerting anti-inflammatory and anti-oxidative stress effects which are mediated by integrated Nrf2, NF-kappaB, and AP-1 signaling pathways. In addition, phytochemicals from herbal medicinal plants and/or some dietary plants developed in recent years have been shown to induce apoptosis in cancer cells and inhibition of tumor growth in vivo. In advanced tumors, a series of changes involving critical signaling molecules that would drive tumor cells undergoing epithelial-mesenchymal transition and becoming invasive. In this review, we will discuss the potential molecular targets and signaling pathways that mediate tumor onset and metastasis. In addition, we will shed light on some of the phytochemicals that are capable of targeting these signaling pathways which would make them potentially applicable to cancer chemoprevention, treatment and control of cancer progression.

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“…They contend that the failure of the Armitage-Doll power law to predict incidence at old age is likely to reflect a problem with cellular theories. However, most other authors (including those who introduced the earliest models), by noting the importance of cohort effects, accepted the difficulty of evaluating cellular mechanisms using population data (Armitage andDoll 1954, 1957;Cook et al 1969). Pompei and Wilson fail to do this.…”

Section: Biological Plausibilitymentioning

confidence: 97%

“…Pompei and Wilson fail to do this. In a 1985 review of multistage models of carcinogenesis, Armitage (1985) comments that, "In many areas of biomathematics the ingenuity of the mathematician often seems to run ahead of the ability of the biological scientist to provide the data needed to validate the mathematical models." Despite their…”

Section: Biological Plausibilitymentioning

confidence: 98%