A theory of the cancer age-specific incidence data based on extreme value distributions

Soto-Ortiz, Luis; Brody, James P.

doi:10.1063/1.3699050

Cited by 12 publications

(12 citation statements)

References 22 publications

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“…A theory of the age-specific incidence curve. We have postulated that the age-specific incidence curve should follow a extreme value distribution, in particular the Weibull distribution [14]. Our reasoning is that:…”

Section: Understanding the Age-specific Incidence Datamentioning

confidence: 98%

The Age Specific Incidence Anomaly Suggests that Cancers Originate During Development

Brody

2014

Biophys. Rev. Lett.

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Cancers are caused by the accumulation of genetic alterations. Since this accumulation takes time, the incidence of most cancers is thought to increase exponentially with age. However, careful measurements of the age-specific incidence shows that the specific incidence for many forms of cancer rises with age to a maximum, then decreases. This decrease in the age-specific incidence with age is an anomaly. Understanding this anomaly should lead to a better understanding of how tumors develop and grow. Here I derive the shape of the age-specific incidence, showing that it should follow the shape of a Weibull distribution. Measurements indicate that the age-specific incidence for colon cancer does indeed follow a Weibull distribution. This analysis leads to the interpretation that for colon cancer two sub-populations exist in the general population: a susceptible population and an immune population. Colon tumors will only occur in the susceptible population. This analysis is consistent with the developmental origins of disease hypothesis and generalizable to many other common forms of cancer.

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Section: Understanding the Age-specific Incidence Datamentioning

confidence: 98%

The Age Specific Incidence Anomaly Suggests that Cancers Originate During Development

Brody

2014

Biophys. Rev. Lett.

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“…The authors [26] emphasised that many different forms for the F i ( t i ) could produce approximately the same observed F ( t ), especially for large n , with the behaviour of F ( t ) being dominated by the small t behaviour of F i ( t ). As a result, for sufficiently small times power-law behaviour for F ( t ) is likely, and if longer times were observable then an extreme value distribution would be expected [4, 26, 27]. However the power-law approximation can fail for important cases with extra rate-limiting steps such as a clonal expansion [5–7].…”

Section: Relation To Recent Multi-stage Cancer Modelsmentioning

confidence: 99%

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Webster

2019

PLoS ONE

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Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

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“…Cancer rates in monozygotic and dizygotic twins differ (1). Similarly, age-specific incidence studies suggest that most cancers occur in small subset of the population, probably determined by inherited genetics (2).…”

Section: Introductionmentioning

confidence: 99%

Chromosomal scale length variation of germline DNA can predict individual cancer risk

Toh

Brody

2018

Preprint

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Abstract:BACKGROUND: Twin studies suggest that inherited factors are responsible for a substantial portion of many different forms of cancer. However, most of these inherited factors have yet to be identified. Most analyses of genome wide association data focus on the additive effects of single nucleotide polymorphisms found in germline DNA. The objective of this study is to test whether germline DNA copy number variation data can be used to predict whether a person will develop cancer.

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A theory of the cancer age-specific incidence data based on extreme value distributions

Cited by 12 publications

References 22 publications

The Age Specific Incidence Anomaly Suggests that Cancers Originate During Development

The Age Specific Incidence Anomaly Suggests that Cancers Originate During Development

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Chromosomal scale length variation of germline DNA can predict individual cancer risk

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