To use or not to use? Backward equations in stochastic carcinogenesis models.

The method based on the Kolmogorov backward equations of Little (1995, Biometrics 51, 1278-1291) for computing hazard functions for the multistage carcinogenesis models fails when model parameters are time-dependent. In addition to suggesting an alternative method based on the Kolmogorov forward equation, this note highlights the interplay of the forward equation, the backward equation, and the characteristic method. Advantages and disadvantages of the forward and backward equations are discussed.