Apply TSCE Carcinogenesis Model into APC Model Sample Clauses

Apply TSCE Carcinogenesis Model into APC Model. The hazard function derived from the TSCE model is introduced to the APC model as well. In contrast to the simple format of the hazard function in the Armitage-Doll model, the hazard function from the TSCE model is more difficult. Four derived parameters will be summarized in the TSCE model, the rate of initiation, ν, the rate of division, α, and death, β, of initial cells, and the rate of malignant conversion, µ. The hazard function in the TSCE model is given by Xxxxxxxxxx [1979, 1981, 1990, 2009] as h(t) = ν e—qt e—pt pq , α qe—pt − pe—qt where p and q are the roots of a quadratic equation, with p + q = −(α − β − µ) and pq = αµ. Three estimated parameters p, q, and r ≡ ν/α will be treated in the model. As we can see, the TSCE model requires one parameter more than the Armitage-Doll model. However, it adds additional complexity to the model, incorporates the stochastic feature of the carcinogenic process and characterizes the kinetics of clonal expansion.