Portier C J, Kopp-Schneider A, Sherman C D
National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina, USA.
Math Biosci. 1996 Jul 15;135(2):129-46. doi: 10.1016/0025-5564(96)00011-9.
Multistage models of carcinogenesis are increasingly used in the estimation of risks from exposure to environmental agents. The two-stage model of carcinogenesis is routinely used because it agrees with much of the existing tumor incidence data, parallels the biological two-stage model, and has much of its mathematical details derived. However, recent findings on the mechanisms of carcinogenesis has led researchers to believe that there are a greater number of stages and a more complex structure to these models than a single pathway. In this paper, a method for readily computing tumor incidence rates for arbitrarily complex multistage models is derived. The formulas for the two-stage model with time-varying rates are given explicitly. Simple rules for more complicated models are given, and computer code able to implement these formulas are provided.
致癌作用的多阶段模型越来越多地用于评估接触环境因素所带来的风险。致癌作用的两阶段模型被常规使用，因为它与许多现有的肿瘤发病率数据相符，与生物学两阶段模型相似，并且其许多数学细节已经推导得出。然而，最近关于致癌机制的研究结果使研究人员相信，这些模型的阶段数量更多，结构比单一途径更复杂。本文推导了一种用于轻松计算任意复杂多阶段模型肿瘤发病率的方法。明确给出了具有随时间变化率的两阶段模型的公式。给出了更复杂模型的简单规则，并提供了能够实现这些公式的计算机代码。
