Armitage-Doll Multistage Model Sample Clauses

Armitage-Doll Multistage Model. In the early 1950s, Armitage and Doll first proposed the multistage model of carcinogenesis which described the quantitative relationship between cancer mortality and age in indus- trialized nations [Armitage and Doll, 1954]. A stochastic model was used to describe the development of a malignant cancer from a normal cell as a finite number of stages on transi- tions. They found that the mortality rate (r) is proportional to age at death (t) raised to a power that is one less than the number of stages (s) between normal health and death, i.e., r = α× ts−1, where α is a proportionality constant. The parameter α is affected by various factors such as gender, race, diet, genetic, environmental factors. This relationship is a di- rect consequence of the properties of a time-homogeneous birth process, the mathematical theory underpinning the multistage model. By taking the logarithm of this relationship we can write log(r) = θ + (s − 1) × log(t) where θ is some unknown constant. Thus the logarithm of the rate increases linearly with the log of age at death, and the slope of this line is s − 1, that is, the number of stages less 1. Specifically Armitage and Doll noted that mortality increased with the sixth power of age, an observation that is consistent with the occurrence of seven successive cellular changes (i.e., stages) leading up to the development of cancer. To derive this mathematical model, Armitage and Doll assumed a constant probability of occurrence of mutation throughout the lifetime and each mutation is a relatively rare event [1954]. Suppose during the time interval [0, t] the probability that mutation i happened i=1 is pit, then the probability that n − 1 mutations happened is Qn pitn−1. If order of n mutations is not considered, there will be (n − 1)! possible orderings of the mutations. (n−1)! i=1