Department of Epidemiology and Public Health, Imperial College, London, UK.
PLoS One. 2009 Dec 31;4(12):e8520. doi: 10.1371/journal.pone.0008520.
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.
Heidenreich 等人（Risk Anal 1997 17 391-399）在双突变癌症模型的背景下考虑了参数可识别性，并证明了模型参数的所有组合中除了两个组合外都是可识别的。我们考虑了 Little 和 Wright（Math Biosci 2003 183 111-134）以及 Little 等人（J Theoret Biol 2008 254 229-238）最近开发的致癌模型中的可识别性问题。这些模型结合了基因组不稳定性，推广了大量其他准生物学癌症模型，特别是 Armitage 和 Doll（Br J Cancer 1954 8 1-12）、双突变模型（Moolgavkar 等人，Math Biosci 1979 47 55-77）、Little 的广义多阶段模型（Biometrics 1995 51 1278-1291）以及 Nowak 等人最近开发的癌症模型（PNAS 2002 99 16226-16231）。
方法/主要发现：我们表明，在 Little 和 Wright 提出的更简单的模型（Math Biosci 2003 183 111-134）中，参数可识别组合的数量最多比生物学参数少两个，从而推广了 Heidenreich 等人（Risk Anal 1997 17 391-399）针对双突变模型的结果。对于 Little 等人的更一般模型（J Theoret Biol 2008 254 229-238），参数可识别组合的数量最多比生物学参数少，其中是失稳类型的数量，从而也推广了所有这些结果。数值评估表明这些界是准确的。我们还确定了可识别参数的特定组合。
结论/意义：我们表明，关于参数可识别性的先前结果可以推广到更大类别的准生物致癌发生模型，并且还确定了可识别参数的特定组合。这些结果具有理论意义，但对于试图为这个大型癌症模型类估计参数的任何人也具有实际意义。
