Identifiability analysis for stochastic differential equation models in systems biology

Browning, Alexander P; Warne, David J.; Burrage, Kevin; Baker, Ruth E.; Simpson, Matthew J.

doi:10.1098/rsif.2020.0652

Cited by 69 publications

(63 citation statements)

References 191 publications

(346 reference statements)

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“…Practical identifiability involves the ability to estimate parameters to sufficient accuracy given finite, noisy data [10,30,37]. Methods of identifiability analysis are often used in the systems biology literature where there are many competing models available to describe similar phenomena [16,33], and these methods provide insight into the trade-off between model complexity and data availability [7]. We also consider the often-neglected question of whether basic statistical assumptions required for the validity of identifiability analysis hold.…”

Section: Introductionmentioning

confidence: 99%

Parameter identifiability and model selection for sigmoid population growth models

Simpson

et al. 2021

Preprint

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Sigmoid growth models, such as the logistic and Gompertz growth models, are widely used to study various population dynamics ranging from microscopic populations of cancer cells, to continental-scale human populations. Fundamental questions about model selection and precise parameter estimation are critical if these models are to be used to make useful inferences about underlying ecological mechanisms. However, the question of parameter identifiability for these models -- whether a data set contains sufficient information to give unique or sufficiently precise parameter estimates for the given model -- is often overlooked; We use a profile-likelihood approach to systematically explore practical parameter identifiability using data describing the re-growth of hard coral cover on a coral reef after some ecological disturbance. The relationship between parameter identifiability and checks of model misspecification is also explored. We work with three standard choices of sigmoid growth models, namely the logistic, Gompertz, and Richards' growth models; We find that the logistic growth model does not suffer identifiability issues for the type of data we consider whereas the Gompertz and Richards' models encounter practical non-identifiability issues, even with relatively-extensive data where we observe the full shape of the sigmoid growth curve. Identifiability issues with the Gompertz model lead us to consider a further model calibration exercise in which we fix the initial density to its observed value, neglecting its uncertainty. This is a common practice, but the results of this exercise suggest that parameter estimates and fundamental statistical assumptions are extremely sensitive under these conditions; Different sigmoid growth models are used within subdisciplines within the biology and ecology literature without necessarily considering whether parameters are identifiable or checking statistical assumptions underlying model family adequacy. Standard practices that do not consider parameter identifiability can lead to unreliable or imprecise parameter estimates and hence potentially misleading interpretations of the underlying mechanisms of interest. While tools in this work focus on three standard sigmoid growth models and one particular data set, our theoretical developments are applicable to any sigmoid growth model and any relevant data set. MATLAB implementations of all software available on GitHub.

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Section: Introductionmentioning

confidence: 99%

Parameter identifiability and model selection for sigmoid population growth models

Simpson

et al. 2021

Preprint

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“…The issue of parameter identifiability has been widely discussed in the literature, with studies suggesting to change, reduce complexity or re-parameterize models (e.g. Browning et al, 2020). Thus, future work needs to evaluate strategies to deal with parameter identifiability issues in agricultural models.…”

Section: Discussionmentioning

confidence: 99%

Considering unknown uncertainty in imperfect models: nitrogen mineralization as a case study

2021

MODSIM2021, 24th International Congress on Modelling and Simulation.

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All models are imperfect, so it is important to consider uncertainty in their predictions. When calibrating models to measured data, uncertainty in the model can be simultaneously estimated, although there are multiple methods available for doing this. In this study, we applied ensemble smoothers and Bayesian inference to calibrate a model of nitrogen mineralization in soils. We obtained mineralization measurements from a previously published study that measured changes in inorganic nitrogen over long-term laboratory incubations in a soil located in the Mackay Whitsundays region (North Queensland). Simulations were performed using the Agricultural Production Systems Simulator (APSIM). We inferred two parameters that characterize the size of the simulated soil organic carbon pools (fbiom and finert) because it is difficult to estimate these parameters from measurements only. For the calibration, we considered two different sources of uncertainty: measurement noise and noise of unknown origin, the latter of which includes all nonmeasurement related errors. We found that ignoring noise of unknown origin can result in an overly optimistic representation of the model error (Figure 1a,c). On the contrary, incorporating noise of unknown origin can lead to a more accurate representation of the uncertainty in the predictions, with model predictions providing adequate coverage of measurements (Figure 1b,d). We show that parameterizing fbiom and finert is difficult because these parameters are correlated, hence different combinations of parameters can equally well simulate the measured data. We suggest that future work needs to provide a means of parameterizing at least one of these fractions independently to facilitate parameter identifiability. Figure 1. Measured (grey dots) and simulated (orange lines) nitrogen mineralization (mg N kg -1 ) for the ensemble smoother with multiple data assimilation (ES-MDA) (a), flexible iterative ES-MDA (b), Bayesian inference with measurement noise only (c), Bayesian inference with measurement noise and additional noise (d). The error bars in the measured data represent the error of the laboratory method. Shaded areas represent the predicted 95% credible intervals.

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“…can make extracting the success of any single measure difficult (Soltesz et al, 2020). Statistical identification of parameters measuring individual impacts will likely be impossible, as structural and practical non-identifiability will be at play without careful experimental design and model sensitivity analysis (Browning et al, 2020). Multiple layers of interventions such as NPIs make the evaluation of these layers individually incredibly difficult as the epidemics evolve, especially as the introduction of subsequent NPIs can impact the efficacy of or adherence to existing interventions.…”

Section: Challenges In Parameter Estimation and Model Fittingmentioning

confidence: 99%

Challenges for modelling interventions for future pandemics

et al. 2022

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Identifiability analysis for stochastic differential equation models in systems biology

Cited by 69 publications

References 191 publications

Parameter identifiability and model selection for sigmoid population growth models

Parameter identifiability and model selection for sigmoid population growth models

Considering unknown uncertainty in imperfect models: nitrogen mineralization as a case study

Challenges for modelling interventions for future pandemics

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