Parameter Identifiability and Redundancy in a General Class of Stochastic Carcinogenesis Models

Background Heidenreich et al. (Risk Anal 1997 17 391–399) considered parameter identifiability in the context of the two-mutation cancer model and demonstrated that combinations of all but two of the model parameters are identifiable. We consider the problem of identifiability in the recently developed carcinogenesis models of Little and Wright (Math Biosci 2003 183 111–134) and Little et al. (J Theoret Biol 2008 254 229–238). These models, which incorporate genomic instability, generalize a large number of other quasi-biological cancer models, in particular those of Armitage and Doll (Br J Cancer 1954 8 1–12), the two-mutation model (Moolgavkar et al. Math Biosci 1979 47 55–77), the generalized multistage model of Little (Biometrics 1995 51 1278–1291), and a recently developed cancer model of Nowak et al. (PNAS 2002 99 16226–16231). Methodology/Principal Findings We show that in the simpler model proposed by Little and Wright (Math Biosci 2003 183 111–134) the number of identifiable combinations of parameters is at most two less than the number of biological parameters, thereby generalizing previous results of Heidenreich et al. (Risk Anal 1997 17 391–399) for the two-mutation model. For the more general model of Little et al. (J Theoret Biol 2008 254 229–238) the number of identifiable combinations of parameters is at most less than the number of biological parameters, where is the number of destabilization types, thereby also generalizing all these results. Numerical evaluations suggest that these bounds are sharp. We also identify particular combinations of identifiable parameters. Conclusions/Significance We have shown that the previous results on parameter identifiability can be generalized to much larger classes of quasi-biological carcinogenesis model, and also identify particular combinations of identifiable parameters. These results are of theoretical interest, but also of practical significance to anyone attempting to estimate parameters for this large class of cancer models.