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Identifiability analysis for stochastic differential equation models in systems biology.

ABSTRACT: Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

SUBMITTER: Browning AP

PROVIDER: S-EPMC7811582 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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Identifiability analysis for stochastic differential equation models in systems biology.

Browning Alexander P AP Warne David J DJ Burrage Kevin K Baker Ruth E RE Simpson Matthew J MJ

Journal of the Royal Society, Interface 20201216 173

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of <i>parameter identifiability</i> have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for dete ...[more]

PMID: 33323054

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Project description:BackgroundHeidenreich 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 findingsWe 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/significanceWe 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.

Project description:ObjectiveOur aim is to analyze the identifiability of three commonly used control-oriented models for glucose control in patients with type 1 diabetes (T1D).MethodsStructural and practical identifiability analysis were performed on three published control-oriented models for glucose control in patients with type 1 diabetes (T1D): the subcutaneous oral glucose minimal model (SOGMM), the intensive control insulin-nutrition-glucose (ICING) model, and the minimal model control-oriented (MMC). Structural identifiability was addressed with a combination of the generating series (GS) approach and identifiability tableaus whereas practical identifiability was studied by means of (1) global ranking of parameters via sensitivity analysis together with the Latin hypercube sampling method (LHS) and (2) collinearity analysis among parameters. For practical identifiability and model identification, continuous glucose monitor (CGM), insulin pump, and meal records were selected from a set of patients (n = 5) on continuous subcutaneous insulin infusion (CSII) that underwent a clinical trial in an outpatient setting. The performance of the identified models was analyzed by means of the root mean square (RMS) criterion.ResultsA reliable set of identifiable parameters was found for every studied model after analyzing the possible identifiability issues of the original parameter sets. According to an importance factor ([Formula: see text]), it was shown that insulin sensitivity is not the most influential parameter from the dynamical point of view, that is, is not the parameter impacting the outputs the most of the three models, contrary to what is assumed in the literature. For the test data, the models demonstrated similar performance with most RMS values around 20 mg/dl (min: 15.64 mg/dl, max: 51.32 mg/dl). However, MMC failed to identify the model for patient 4. Also, considering the three models, the MMC model showed the higher parameter variability when reidentified every 6 hours.ConclusionThis study shows that both structural and practical identifiability analysis need to be considered prior to the model identification/individualization in patients with T1D. It was shown that all the studied models are able to represent the CGM data, yet their usefulness in a hypothetical artificial pancreas could be a matter of debate. In spite that the three models do not capture all the dynamics and metabolic effects as a maximal model (ie, our FDA-accepted UVa/Padova simulator), SOGMM and ICING appear to be more appealing than MMC regarding both the performance and parameter variability after reidentification. Although the model predictions of ICING are comparable to the ones of the SOGMM model, the large parameter set makes the model prone to overfitting if all parameters are identified. Moreover, the existence of a high nonlinear function like [Formula: see text] prevents the use of tools from the linear systems theory.

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Identifiability analysis for stochastic differential equation models in systems biology.

Publications

Identifiability analysis for stochastic differential equation models in systems biology.

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