Dataset Information

Parameter identifiability and redundancy in a general class of stochastic carcinogenesis models.

ABSTRACT:

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.

SUBMITTER: Little MP

PROVIDER: S-EPMC2797326 | biostudies-literature | 2009 Dec

REPOSITORIES: biostudies-literature

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Publications

Parameter identifiability and redundancy in a general class of stochastic carcinogenesis models.

Little Mark P MP Heidenreich Wolfgang F WF Li Guangquan G

PloS one 20091231 12

<h4>Background</h4>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, generali ...[more]

PMID: 20046831

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Project description:BackgroundKinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.MethodsWe present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.ResultsOur contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub ( https://github.com/gabora/visid ).ConclusionsOur approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.

Dataset Information

Parameter identifiability and redundancy in a general class of stochastic carcinogenesis models.

Background

Methodology/principal findings

Conclusions/significance

Publications

Parameter identifiability and redundancy in a general class of stochastic carcinogenesis models.

Similar Datasets

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