On a trinity role of the survival and hazard functions of the two-stage carcinogenesis models

Three types of the two-stage models that were based on the linear birth-and-death processes were originally envisioned by Kendall (1960) as tools for modeling the carcinogenic process. While two of the three models enjoy widespread applicability, the other has lain fallow so far. This note reports that, as far as the survival and hazard functions are concerned, all three models are equivalent. In addition to giving a proof of the claim, the note also discusses some of the implications within the context of applications of the two-stage models.