Two-Stage Clonal Expansion TSCE Model

The standard measure for cancer risk is the hazard or age-specific incidence function of cancer. Let T be the time to malignant transformation of a particular tissue. Let P t) = E[r f] be the probability that cancer occurs before age t. Then, the hazard or incidence function is defined as 

the hazard measures the instantaneous rate at which cancer occurs in a previously cancer free tissue. The hazard can be expressed also in terms of the survival function, S(t) = P[T T] = 1 - P t), 

The statistical estimator for the hazard is the ineidence or mortahty rate of cancer in a population (number of cases/population at risk). 

The two-stage clonal expansion model (TSCE) was originally developed by Moolgavkar and Venzon (1979) and Moolgavkar and Knudson (1981). This model assumes that malignant transformation of susceptible stem cells oeeurs as a result 

Constant Model Parameters. If we assume that the number of susceptible stem cells is constant during life and that the model parameters are constant, then we can find a closed-form expression for the hazard and survival function under the TSCE model (Luebeck and Moolgavkar 2002)  

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