### Abstract

Modeling of cancer hazards at age t deals with a dichotomous population, a small part of which (the fraction at risk) will get cancer, while the other part will not. Therefore, we conditioned the hazard function, h(t), the probability density function (pdf), f(t), and the survival function, S(t), on frailty α in individuals. Assuming α has the Bernoulli distribution, we obtained equations relating the unconditional (population level) hazard function, h_{U}(t), cumulative hazard function, H_{U}(t), and overall cumulative hazard, H_{0}, with the h(t), f(t), and S(t) for individuals from the fraction at risk. Computing procedures for estimating h(t), f(t), and S(t) were developed and used to fit the pancreatic cancer data collected by SEER9 registries from 1975 through 2004 with the Weibull pdf suggested by the Armitage-Doll model. The parameters of the obtained excellent fit suggest that age of pancreatic cancer presentation has a time shift about 17 years and five mutations are needed for pancreatic cells to become malignant.

Original language | English (US) |
---|---|

Pages (from-to) | 67-81 |

Number of pages | 15 |

Journal | Cancer Informatics |

Volume | 12 |

DOIs | |

State | Published - Feb 27 2013 |

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### Keywords

- Cancer hazard
- Cancer incidence
- Frailty
- Pancreatic cancer
- Weibull distribution

### ASJC Scopus subject areas

- Oncology
- Cancer Research

### Cite this

**Basic equations and computing procedures for frailty modeling of carcinogenesis : Application to pancreatic cancer data.** / Mdzinarishvili, Tengiz; Sherman, Simon.

Research output: Contribution to journal › Article

*Cancer Informatics*, vol. 12, pp. 67-81. https://doi.org/10.4137/CIN.S8063

}

TY - JOUR

T1 - Basic equations and computing procedures for frailty modeling of carcinogenesis

T2 - Application to pancreatic cancer data

AU - Mdzinarishvili, Tengiz

AU - Sherman, Simon

PY - 2013/2/27

Y1 - 2013/2/27

N2 - Modeling of cancer hazards at age t deals with a dichotomous population, a small part of which (the fraction at risk) will get cancer, while the other part will not. Therefore, we conditioned the hazard function, h(t), the probability density function (pdf), f(t), and the survival function, S(t), on frailty α in individuals. Assuming α has the Bernoulli distribution, we obtained equations relating the unconditional (population level) hazard function, hU(t), cumulative hazard function, HU(t), and overall cumulative hazard, H0, with the h(t), f(t), and S(t) for individuals from the fraction at risk. Computing procedures for estimating h(t), f(t), and S(t) were developed and used to fit the pancreatic cancer data collected by SEER9 registries from 1975 through 2004 with the Weibull pdf suggested by the Armitage-Doll model. The parameters of the obtained excellent fit suggest that age of pancreatic cancer presentation has a time shift about 17 years and five mutations are needed for pancreatic cells to become malignant.

AB - Modeling of cancer hazards at age t deals with a dichotomous population, a small part of which (the fraction at risk) will get cancer, while the other part will not. Therefore, we conditioned the hazard function, h(t), the probability density function (pdf), f(t), and the survival function, S(t), on frailty α in individuals. Assuming α has the Bernoulli distribution, we obtained equations relating the unconditional (population level) hazard function, hU(t), cumulative hazard function, HU(t), and overall cumulative hazard, H0, with the h(t), f(t), and S(t) for individuals from the fraction at risk. Computing procedures for estimating h(t), f(t), and S(t) were developed and used to fit the pancreatic cancer data collected by SEER9 registries from 1975 through 2004 with the Weibull pdf suggested by the Armitage-Doll model. The parameters of the obtained excellent fit suggest that age of pancreatic cancer presentation has a time shift about 17 years and five mutations are needed for pancreatic cells to become malignant.

KW - Cancer hazard

KW - Cancer incidence

KW - Frailty

KW - Pancreatic cancer

KW - Weibull distribution

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UR - http://www.scopus.com/inward/citedby.url?scp=84874202632&partnerID=8YFLogxK

U2 - 10.4137/CIN.S8063

DO - 10.4137/CIN.S8063

M3 - Article

C2 - 23471174

AN - SCOPUS:84874202632

VL - 12

SP - 67

EP - 81

JO - Cancer Informatics

JF - Cancer Informatics

SN - 1176-9351

ER -