A new look at multi-stage models of cancer incidence

Multi-stage models have long been used in combination with SEER data to make inferences about the mechanisms underlying cancer initiation. The main method for studying these models mathematically has been the computation of generating functions by solving hyperbolic partial differential equations. Here, we analyze these models using a probabilistic approach similar to the one Durrett and Moseley [7] used to study branching process models of cancer. This more intuitive approach leads to simpler formulas and new insights into the behavior of these models. Unfortunately, the examples we consider suggest that fitting multi-stage models has very little power to make inferences about the number of stages unless parameters are constrained to take on realistic values.