A note on approximating the cumulative distribution function of the time to tumor onset in multistage models.

The general multistage theory of carcinogenesis is a very special type of interconnected birth and death process in which the final state is absorbing and all states except the first one are empty at time zero. An approximation proposed by Whittemore and Keller (1978, SIAM Review 20, 1-30) is assessed. It is shown that the adequacy of this approximation depends on the number of malignant cells resulting from a single normal cell. If more than one malignant cell is likely to occur, the approximation will fail.