Abstract
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.
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Notes
The authors wish to thank Prof. Marek Kimmel and Prof. Maia Martcheva for their careful reading and helpful comments and suggestions. The authors also wish to thank the anonymous referee for helping to greatly improve the content of the paper and for providing the inspiration for Theorem 10.
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Hiller, J., Keesling, J. Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis. Bull Math Biol 80, 670–686 (2018). https://doi.org/10.1007/s11538-018-0397-3
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DOI: https://doi.org/10.1007/s11538-018-0397-3