Bulletin of Mathematical Biology

, Volume 80, Issue 3, pp 670–686 | Cite as

Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis

  • Josh Hiller
  • James Keesling
Original Article


We examine basic asymptotic properties of relative risk for two families of generalized Erlang processes (where each one is based off of a simplified Armitage and Doll multistage model) in order to predict relative risk data from cancer. The main theorems that we are able to prove are all corroborated by large clinical studies involving relative risk for former smokers and transplant recipients. We then show that at least some of these theorems do not extend to other Armitage and Doll multistage models. We conclude with suggestions for lifelong increased cancer screening for both former smoker and transplant recipient subpopulations of individuals and possible future directions of research.


Relative risk Multistage model Erlang distribution Cancer Smoking Transplant 


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAdelphi UniversityGarden CityUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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