Analysis of Premalignant Lesions Using the TSCE Model

Analysis of Premalignant Lesions Using the TSCE Model 

In several cancers, premalignant lesions appear long before the clinical onset of the disease. Examples of these are the aberrant crypts foci (ACF) and the adenomatous polyps that appear in the colon and which are considered to be precursors of colorec- 

Several expressions for the number and size of premalignant lesions undo-different scenarios have been derived in the past (Dewanji et al. 1989, 2005 Jeon et al. 2008 Moolgavkar and Luebeck 1990). We briefly describe some of the mathematical formulas for the number and size distributions of premalignant lesions and the total number of premalignant cells under the TSCE model. 

Constant Parameters. Let N(t) represent the number of non-extinct premalignant lesions at time t. Then N(t) is a Poisson random variable with expectation A(t), where (Dewanji et al. 1989) 

Minimum Detection Threshold. Since in reality, premalignant lesions can be detected only when they are larger than a certain size, Dewanji et al. also derived expressions for the number and size of detectable premalignant lesions assuming a detection threshold size o (Dewanji et al. 1989). Assuming that a and j8 are constant, the number of detectable premalignant lesions at time t, say is a Poisson random variable with expectation A (i)  

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