Department of Mathematics and Computer Science, Adelphi University, P.O. Box 118105, Garden City, NY, 11530, USA.
Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL, 32611-8105, USA.
Bull Math Biol. 2018 Mar;80(3):670-686. doi: 10.1007/s11538-018-0397-3. Epub 2018 Jan 30.
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.
我们研究了两种广义 Erlang 过程（其中每一种都基于简化的 Armitage 和 Doll 多阶段模型）的相对风险的基本渐近性质，以便从癌症中预测相对风险数据。我们能够证明的主要定理都得到了涉及前吸烟者和移植受者相对风险的大型临床研究的证实。然后，我们表明，至少其中一些定理不适用于其他 Armitage 和 Doll 多阶段模型。最后，我们为前吸烟者和移植受者这两个人群提出了终生增加癌症筛查的建议，并提出了可能的未来研究方向。
