| Summary: | 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 ft 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.
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