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Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood
Open accessAbstract
MOTIVATION: Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. RESULTS: We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction. AVAILABILITY: An implementation is freely available for MATLAB and the PottersWheel modeling toolbox at http://web.me.com/andreas.raue/profile/software.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
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TL;DR
The paper presents a profile-likelihood method for assessing structural and practical identifiability in partially observed dynamical models and for deriving likelihood-based confidence intervals. Applied to a JAK-STAT signaling model, it identifies four structurally non-identifiable parameters and one practically non-identifiable parameter, and shows how additional measurements can resolve these ambiguities.
Key findings
- Profile likelihood distinguishes structural non-identifiability, seen as a flat profile, from practical non-identifiability, seen as a profile with a minimum that fails to cross the confidence threshold in one or both directions; identifiable parameters cross the threshold on both sides.
- In the JAK-STAT application, parameters p2, x1(0), s1, and s2 were structurally non-identifiable, with functional relations p2·x1(0)=const, s1·x1(0)=const, and s2·x1(0)=const; p3 was practically non-identifiable for increasing values.
- Table 1 reports infinite likelihood-based intervals for the structurally non-identifiable parameters, whereas Hessian-based asymptotic intervals were finite but misleadingly narrow, e.g. p2: −33 to +31, x1(0): −31 to +32, s1: −32 to +31, s2: −32 to +31; for p3, the profile-likelihood interval was −1.14 to +∞ versus −1.14 to +0.15 from the Hessian.
- Adding hypothetical measurements of x1(0)=200±20 nM and x3/(x2+x3)=0.90±0.05 at t=20 min made p2, x1(0), s1, and s2 structurally identifiable and p3 practically identifiable, while p2 remained practically non-identifiable. Profile-likelihood computation took 54±18 s per parameter on a 1 GHz CPU with 2 GB RAM.
Methods
- The approach uses an ODE model with weighted least-squares objective χ², computes the profile likelihood for each parameter by re-optimizing all other parameters at fixed values of the target parameter, and derives likelihood-based confidence intervals from χ² thresholds.
- The application is a JAK-STAT signaling model inspired by Swameye et al., calibrated to experimental data; observables are phosphorylated STAT in cytoplasm (y1) and total STAT in cytoplasm (y2) measured by quantitative western blotting, with cytoplasm and nucleus volumes of 1400 µm³ and 450 µm³.
- Parameters calibrated include p1–p4, s1, s2, and x1(0), with x2(0)–x4(0) set to zero; the model was implemented and fitted with PottersWheel, and experimental planning and model reduction were explored via profile-likelihood trajectories, Monte Carlo simulations, and likelihood-ratio thresholds.
Limitations
- The authors state that structural non-identifiability cannot be resolved by refining existing measurements or reducing noise; it requires a qualitatively new measurement that changes the observation mapping, such as observing additional species. Practical non-identifiability can be resolved by increasing the amount or quality of data and/or selecting better measurement time points.
- The authors note that recovering functional relations unambiguously from parameter changes along the profile likelihood is only possible when the corresponding manifold is one-dimensional; higher-dimensional manifolds require further analysis, such as the approach of Hengl et al.
- Evident from the text: the method is demonstrated on a single JAK-STAT model and dataset, with no broad empirical comparison across many model classes; the approach also assumes a sufficiently adequate model and normally distributed measurement noise.
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In the paper
“The largest discrepancy occurs for practically non-identifiable parameters, where asymptotic confidence intervals are significantly smaller than likelihood-based confidence intervals.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The variability of the predicted model observables y along the profile likelihood of p 3 remains consistent with the measurement errors, as shown in Figure 6.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The resulting plots of profile likelihood versus parameter reveal four structurally non-identifiable parameters p 2 , x 1 (0), s 1 , s 2 by their flat profile likelihood, see Figure 3, upper panel.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
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In the paper
“For identifiable parameters the discrepancies are small.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The functional relations h connecting these structurally non-identifiable parameters can be recovered from the changes of the remaining parameters, while calculating the profile likelihood of the structurally non-identifiable parameters, as shown in Figure 4.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The recalculated profile likelihood reveals, that parameters p 2 , x 1 (0), s 1 , s 2 become structurally identifiable (Fig. 3, lower panel), by measuring only one of them.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“The profile likelihood reveals that parameter p 3 is practically non-identifiable for increasing parameter values.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: An appropriate model M that sufficiently describes the available experimental data is assumed.
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In the paper
“Nevertheless, a lower confidence bound can be derived.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this case, asymptotic approximation leads to large but nevertheless finite confidence intervals for the structurally non-identifiable parameters.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“All internal model states can only be identified up to a common factor.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“An approach to detect structural non-identifiability by the corresponding functional relations was introduced by Hengl et al. (2007).It is able to detect flatness of likelihood for arbitrary models, but it is not intended to detect practical non-identifiability.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
- Partly supportedcites Hengl et al., 2007 sourceExperimental — accuracy not yet measured
The Approach and Conclusion describe detecting structural non-identifiability through functionally related parameters in nonlinear models. But the Introduction explicitly lists practical identifiability analysis, accounting for data quality, as an aim of the method, contrary to the claim that it is not intended for that purpose. The passages do not specifically describe the method as detecting likelihood flatness. (LLM, conf=0.90)
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In the paper
“Spots of largest variability suggest where and when a measurement of a species most efficiently determines theses parameters: x 1 at times t = 0 or t > 50; x 2 to x 4 at times 5 < t < 30.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“Calculating the profile likelihood takes 54 ± 18 s per parameter, using an implementation of the approach embedded in the Potters-Wheel fitting toolbox (1 GHz CPU, 2 GB RAM), which is described in the Supplementary Material.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
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In the paper
“Parameter p 3 becomes practically identifiable, only previously structurally non-identifiable parameter p 2 remains practically non-identifiable.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“The trajectories of the internal model states x along the profile likelihood of the practically non-identifiable parameter p 3 shown in Figure 6 comprises large antipodal variability of species x 2 and x 3 , revealing that the experimental setup is inappropriate to estimate this parameter with confidence.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“h 1 (θ sub ) = p 2 •x 1 (0)-const = 0 h 2 (θ sub ) = s 1 •x 1 (0)-const = 0 ( 1 1 ) h 3 (θ sub ) = s 2 •x 1 (0)-const = 0”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The approach was applied to a model of the JAK-STAT signaling pathway.Non-identifiable parameters were detected, revealing limitations in the experimental setup.Additional measurements that efficiently improve parameter identification were suggested and validated.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“They are exact if the observables y depend linearly on θ.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
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In the paper
“Unfortunately, these methods become rapidly infeasible with increasing model size (Margaria et al., 2001;White et al., 2001).Practical non-identifiability cannot be detected, since experimental data are disregarded.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
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In the paper
“Even identifiable parameters can only be determined within confidence intervals, which contain the true value of the parameter with a desired probability (Lehmann and Leo, 1983).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 1 INTRODUCTION
What the sources say
- Not matchedcites Lehmann and Leo, 1983
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In the paper
“These methods are appropriate if functional relations h between the parameters emerging from structural non-identifiability are linear.This is often not the case for reaction networks modeled by ODE, because observables depend non-linearly on the parameters.Practical non-identifiability cannot be detected, because a quadratic approximation is not able to explain increasing but limited behavior of”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
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In the paper
“However, even for the simplest reaction network the observables y depend nonlinearly on θ and the amount and quality of experimental data is often insufficient.Therefore, asymptotic confidence intervals might not be appropriate (Joshi et al., 2006).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Joshi et al., 2006 source
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In the paper
“Likelihood-based confidence intervals are considered superior to asymptotic confidence intervals for finite samples (Neale and Miller, 1997).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.2 Finite sample confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Neale and Miller, 1997 source
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In the paper
“Along a practical non-identifiability, the observable y change only negligibly remaining compliant with the given measurement accuracy.Nevertheless, model behavior in terms of internal states x might vary strongly.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > )]:
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In the paper
“This arises frequently if amount and quality of experimental data is insufficient and manifests in a confidence interval that is infinite.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.3.2 Practical non-identifiability
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In the paper
“The points of passover represent likelihoodbased confidence intervals as defined in Equation ( 8) (Royston, 2007).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
What the sources say
- Not checked — no full text of the sourcecites Royston, 2007 source
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In the paper
“The results are easy to interpret”
- Also stated in: § 6 DISCUSSION · plain
“The approach results in easily interpretable plots of profile likelihood versus parameter.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Abstract
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- Also stated in: § 6 DISCUSSION · plain
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In the paper
“The profile likelihood of a practically non-identifiable parameter has a minimum, but is not excessing a threshold α for increasing and/or decreasing values of θ i (see Definition 1).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
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In the paper
“This gives insight into a complex and high-dimensional parameter space.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“It can be automated, but an explicit advantage is that the output might be evaluated visually.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“The approach can be applied to any parameter estimation problem, where a likelihood or a similar objective criterion is available, e.g.partial differential equations (PDE) or stochastic differential equations (SDE).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“The profile likelihood can be calculated for each parameter separately.Thereby it is possible to restrict the analysis to the parameters relevant for the biological question.Moreover, this allows to perfectly parallelize the approach, which is a major benefit for its scalability.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“Working in logarithmic parameter space linearizes the functional relations given in Equation (11).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The impact of new measurements can be evaluated by Monte Carlo simulations.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“Thus, identifiability analysis ensures that the model complexity is tailored to the information content given by the experimental data.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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The authors state this as an assumption.
The measurement noise is normally distributed.
“The measurement noise (t) is assumed to be normally distributed.”
The authors state this as an assumption.
An appropriate model M that sufficiently describes the available experimental data is assumed.
“Furthermore, an appropriate model M that sufficiently describes the available experimental data is assumed.”
The paper relies on this without support.
No approach for explicit testing of practical non-identifiability is available.
“Similar to a clear formal definition, an approach for explicit testing of practical non-identifiability is not available to our knowledge.”
The authors state this as an assumption.
The initial values of species x2 to x4 are equal to zero.
“The initial values of species x 2 to x 4 are assumed to be equal to zero.”
The authors state this as an assumption.
For the model-reduction argument, a parameter θi is practically non-identifiable for decreasing parameter value.
“Assume that a parameter θ i is practically non-indentifiable for decreasing parameter value.”
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In the citing paper
“Such parameter estimations usually yield statistical information related to parameter precision (importantly, not accuracy) such as standard errors or correlation matrices, and sometimes information derived from more sophisticated approaches such as profile likelihood.39”
From Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network (2019) · cites this paper as [39]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Raue et al. (2009) referred to likelihood ratio C.I.s as finite sample C.I.s, to underscore the superiority of likelihood ratio C.I.s over Wald-type C.I.s.”
From rSalvador: An R Package for the Fluctuation Experiment (2017) · cites this paper as Raue et al. 2009
In the citing paper
“When two models are nested (Mð hPL Þ and Mð hopt Þ) their likelihood ratio is approximately distributed according to a v 2 p distribution.Here p refers to the number of degrees of freedom which is defined as the difference in the number of parameters (which in this case is 1).”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“In such cases, more reliable confidence intervals can be obtained using the Profile Likelihood method [36].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Techniques for this exist in both a frequentist [13,36,91] as well as a Bayesian setting [87,90].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Fortunately, recent literature is correcting this (e.g. [129–140]).”
From Reverse engineering and identification in systems biology: strategies, perspectives and challenges (2014) · cites this paper as [133]
In the citing paper
“Given the data, not all parameters are identifiable (Raue et al., 2009).”
From A bayesian approach to targeted experiment design (2012) · cites this paper as Raue et al., 2009
In the citing paper
“Methods for an approximate sampling of the parameter space, e.g. the Markov Chain Monte Carlo (MCMC) methods [11,12], and bootstrap based approaches [4,13] are numerically demanding and provide only rough approximations for ODE models. Therefore, it is difficult to control the coverage of the prediction confidence intervals for such approaches.”
From Likelihood based observability analysis and confidence intervals for predictions of dynamic models (2012) · cites this paper as [4]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Concentration unit conflicts with figure labels
MinorThe text says concentrations are modeled in nanometers, a unit of length, while the figure labels use nM, a unit of concentration.
“Species concentrations are modeled in nanometer.”
“time / min x 1 / nM”
Citations
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A robust and efficient algorithm to find profile likelihood confidence intervals
Fischer, S., & Lewis, M. A. (2021) · Statistics and Computing · doi:10.1007/s11222-021-10012-y · Cited by 18
“…Biological Sciences, University of Alberta, CW 405, Biological Sciences Building, Edmonton, AB T6G 2E9, Canada issues occur if not enough data are available to infer a statistical parameter on the desired confidence level, and the corresponding confidence intervals are infinite (Raue et al. 2009).”
BackgroundMethodInfluentialSpiegler, A., Abadchi, J. K., Mohajerani, M. H., & Jirsa, V. (2020) · Network Neuroscience · doi:10.1162/netn_a_00152 · Cited by 15
“Q2 Such inversion analysis relies on all cases on the model in use, the inversion data features, and the model’s identifiability (Raue et al., 2009).”
Schmiester, L., Weindl, D., & Hasenauer, J. (2020) · Journal of Mathematical Biology · doi:10.1007/s00285-020-01522-w · Cited by 15
Identifiability of a Binomial Synapse
Gontier, C., & Pfister, J.-P. (2020) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2020.558477 · Cited by 15
A MATLAB toolbox for modeling genetic circuits in cell-free systems†
Singhal, V., Tuza, Z. A., Sun, Z. Z., & Murray, R. M. (2021) · Synthetic Biology · doi:10.1093/synbio/ysab007 · Cited by 14
“There are a total of 26 parameters in these models, of which several are nonidentifiable [26], [27].”
BackgroundIdentifiability of car-following dynamics
Wang, Y., Monache, M. L. D., & Work, D. B. (2021) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2021.133090 · Cited by 15
“The numerical methods can be used to explore the profile likelihood [32,58], which allows to derive likelihood-based confidence intervals for each parameter and recovers the functional relations between parameters due to non-identifiability.”
MethodMathematical modeling and dynamical analysis of anti-tumor drug dose-response
Xiao, Y., Shen, J., & Zou, X. (2022) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2022190 · Cited by 15
Quantifying the contribution of triglycerides to metabolic resilience through the mixed meal model
O’Donovan, S. D., Erdõs, B., Jacobs, D. M., Wanders, A. J., Thomas, E. L., Bell, J. D., Rundle, M., Frost, G. S., Arts, I. C. W., Afman, L. A., et al. (2022) · iScience · doi:10.1016/j.isci.2022.105206 · Cited by 14
Characterizability of metabolic pathway systems from time series data
Voit, E. O. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.01.008 · Cited by 15
“Some of its difficulties are of computational nature, while others are due to the noisiness of biological data and the fact that several computed solutions often lead to similarly good data fits [6–11].”
BackgroundStructural vs Practical Identifiability of Nonlinear Differential Equation Models in Systems Biology
Saccomani, M. P., & Thomaseth, K. (2016) · Springer eBooks · doi:10.1007/978-3-319-45723-9_3 · Cited by 14
Mangold, M., Khlopov, D., Temmel, E., et al. (2016) · Chemical Engineering Science · doi:10.1016/j.ces.2016.11.042 · Cited by 15
Robust parameter estimation of car-following models considering practical non-identifiability
Monteil, J., & Bouroche, M. (2016) · IEEE International Conference on Intelligent Transportation Systems (ITSC) · doi:10.1109/itsc.2016.7795612 · Cited by 17
“This is known as the technique of the profile likelihood [29], and is commonly used to investigate practical identifiability [14], [30].”
BackgroundMethodInfluentialEstimability and dependency analysis of model parameters based on delay coordinates
Schumann-Bischoff, J., Luther, S., & Parlitz, U. (2016) · Physical review. E · doi:10.1103/physreve.94.032221 · Cited by 15
Cheng, Z., Ronen, A., & Yuan, H. (2023) · ACS ES&T Water · doi:10.1021/acsestwater.3c00131 · Cited by 16
Mechanistic modeling of lipid nanoparticle formation for the delivery of nucleic acid therapeutics
Inguva, P., Mukherjee, S., Walker, P. J., Tenberg, V., Devos, C., Shin, S., Wu, Y., Santra, S., Wang, J., Singh, S., et al. (2025) · Biotechnology Advances · doi:10.1016/j.biotechadv.2025.108643 · Cited by 19
Pöhlmann, J., Smith‐Palmer, J., Serné, E. H., Tuomaala, A., JENDLE, J. H., Choudhary, P., Bosi, E., Mohan, V., van den Heuvel, T. R. A., Cohen, O., et al. (2025) · Diabetes Obesity and Metabolism · doi:10.1111/dom.70161 · Cited by 21
“53 Test statistics and CIs for fixed AID system effects were computed using t-tests, for an alpha level of 0.05 (unless specified differently, “ significant ” in this paper refers to statistical significance at an alpha level of 0.05).”
InfluentialExploiting intrinsic fluctuations to identify model parameters
Zimmer, C., Sahle, S., & Pahle, J. (2015) · IET Systems Biology · doi:10.1049/iet-syb.2014.0010 · Cited by 11
Model Extension and Model Selection
Sunnåker, M., & Stelling, J. (2015) · Studies in mechanobiology, tissue engineering and biomaterials · doi:10.1007/978-3-319-21296-8_9 · Cited by 14
“To our knowledge this procedure has also not yet been tested in practice, but it was discussed as a potential model reduction approach [41].”
MethodBorisov, I. I., & Metelkin, E. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008495 · Cited by 14
“The authors of the study [5] define practical identifiability on the basis of profile likelihood notion: identifiable parameter is one that has finite profile likelihood-based confidence interval.”
BackgroundMethodInfluentialMaking Predictions Using Poorly Identified Mathematical Models
Simpson, M. J., & Maclaren, O. J. (2024) · Bulletin of Mathematical Biology · doi:10.1007/s11538-024-01294-0 · Cited by 14
“Before presenting the PWA details, we first provide some background about these mathematical models and briefly discuss some application areas that motivate their use.”
BackgroundChowell, G., & Skums, P. (2024) · Physics of Life Reviews · doi:10.1016/j.plrev.2024.10.011 · Cited by 14
Calibrating Parameters for Microsimulation Disease Models
van der Steen, A., van Rosmalen, J., Kroep, S., et al. (2016) · Medical Decision Making · doi:10.1177/0272989x16636851 · Cited by 14
“For the calculation of confidence intervals in microsimulation, one can use Bayesian statistics(38) or a profile likelihood approach.(34,39) To ensure the correct coverage of these confidence intervals, the GOF criterion should be based on the likelihood function; there is generally no theoretical support for the calc…”
MethodSchmidt, P. J., Emelko, M. B., & Thompson, M. E. (2019) · Risk Analysis · doi:10.1111/risa.13386 · Cited by 14
“Raue et al. (2009) also discuss “practical nonidentifiability,” where weak information about a parameter that is technically identifiable leads to a profile likelihood that has a unique maximum but diminishes to a high plateau in one direction or the other.”
BackgroundInfluentialAssessment of the parameter identifiability of population balance models for air jet mills
Bhonsale, S. S., Stokbroekx, B., & van Impe, J. F. M. (2020) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2020.107056 · Cited by 14
Neubauer, P. B., Anane, E., Junne, S. G., & Bournazou, M. N. C. (2020) · Advances in biochemical engineering, biotechnology · doi:10.1007/10_2020_154 · Cited by 15
A robust algorithm to test the observability of large linear systems with unknown parameters
Shi, X. F., Williams, M. S., & Chatzis, M. N. (2021) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2021.107633 · Cited by 14
Carr, M. J., Simpson, M. J., & Drovandi, C. (2021) · Journal of The Royal Society Interface · doi:10.1098/rsif.2021.0362 · Cited by 13
Dray, K. E., Muldoon, J. J., Mangan, N. M., Bagheri, N., & Leonard, J. N. (2022) · ACS Synthetic Biology · doi:10.1021/acssynbio.1c00528 · Cited by 13
Evangelou, N., Wichrowski, N. J., Kevrekidis, G. A., Dietrich, F., Kooshkbaghi, M., McFann, S. E., & Kevrekidis, I. G. (2022) · PNAS Nexus · doi:10.1093/pnasnexus/pgac154 · Cited by 14
Strategic model reduction by analysing model sloppiness: A case study in coral calcification
Vollert, S. A., Drovandi, C., Monsalve-Bravo, G. M., et al. (2022) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2022.105578 · Cited by 14
“So, when considering the aggregate behaviour of these processes within the coral polyp, including these “redundant” physiological processes may not lead to better predictions because of structural and/or practical identifiability issues, and instead may cause poor parameter estimation (Raue et al., 2009).”
BackgroundPort, A., Bryan, K. R., Pilditch, C. A., Hamilton, D. P., & Bischof, K. (2015) · Ecological Modelling · doi:10.1016/j.ecolmodel.2015.05.034 · Cited by 13
Markovetz, M. R., Corcoran, T. E., Locke, L. W., Myerburg, M. M., Pilewski, J. M., & Parker, R. S. (2014) · PLoS ONE · doi:10.1371/journal.pone.0111972 · Cited by 13
“there is insufficient data to inform this parameter) over the timescale examined in the present work [22].”
BackgroundParameter Estimation and Identifiability of Biological Networks Using Relative Data
Weber, P., Hasenauer, J., Allgöwer, F., & Radde, N. E. (2011) · IFAC Proceedings Volumes · doi:10.3182/20110828-6-it-1002.01007 · Cited by 14
“This is a special case of the standard ML estimation for ODE systems (Raue et al., 2009; Engl et al., 2009; Balsa-Canto et al., 2008), for which we show that due to the particular problem structure a tremendous reduction of the computational effort can Copyright by the International Federation of…”
BackgroundMethodInfluentialMischnik, M., Hubertus, K., Geiger, J., et al. (2013) · Molecular BioSystems · doi:10.1039/c3mb70142e · Cited by 14
Self-citationRomain, B., Rouet, L., Ohayon, D., Lucidarme, O., d’Alché–Buc, F., & Letort, V. (2016) · Medical Image Analysis · doi:10.1016/j.media.2016.07.008 · Cited by 14
Wei, Y., Kuzmič, P., Yu, R., et al. (2016) · Biochemistry · doi:10.1021/acs.biochem.6b00265 · Cited by 14
Thakre, N., Fernandes, P., Mueller, A., & Graw, F. (2018) · Frontiers in Microbiology · doi:10.3389/fmicb.2018.00166 · Cited by 14
“The 95%-confidence intervals, as well as identifiability of parameter estimates were assessed by profile likelihood analysis (Raue et al., 2009).”
BackgroundMethodKelemen, R. K., Rajakaruna, H., Cockburn, I., & Ganusov, V. (2018) · bioRxiv · doi:10.3389/fimmu.2019.02153 · Cited by 17
He, Q., & Wang, J. (2020) · Processes · doi:10.3390/pr8080951 · Cited by 17
“The confidence interval of a parameter estimate θ̂i can be estimated asymptotically or based on maximum likelihood estimation [83,90].”
InfluentialProfile likelihood analysis for a stochastic model of diffusion in heterogeneous media
Simpson, M. J., Browning, A. P., Drovandi, C., Carr, E. J., Maclaren, O. J., & Baker, R. E. (2021) · QUT ePrints (Queensland University of Technology) · Cited by 13
Porthiyas, J., Nussey, D., Beauchemin, C. A. A., Warren, D. C., Quirouette, C., & Wilkie, K. P. (2024) · npj Systems Biology and Applications · doi:10.1038/s41540-024-00409-6 · Cited by 13
“We used a Markov chain Monte Carlo (MCMC) method to sample and ultimately estimate the posterior likelihood distribution (hereafter Posterior) of each MM ’ s parameters from Bayes ’ theorem.”
BackgroundMethodHock, S., Hasenauer, J., & Theis, F. J. (2013) · BMC Bioinformatics · doi:10.1186/1471-2105-14-s10-s7 · Cited by 13
“While quantitative modeling with ordinary differential equations (ODEs) is a common method and the theory of parameter estimation and identifiability is sound, those results have yet to be transferred to the quantitative modeling with PDEs [9,10].”
BackgroundMethodInfluentialA simple method for identifying parameter correlations in partially observed linear dynamic models
Li, P., & Vu, Q. D. (2015) · BMC Systems Biology · doi:10.1186/s12918-015-0234-3 · Cited by 11
Systems modelling ageing: from single senescent cells to simple multi-cellular models
Guimera, A. M., Welsh, C., Pezze, P. D., Fullard, N., Nelson, G., Roger, M., Przyborski, S. A., & Shanley, D. P. (2017) · Essays in Biochemistry · doi:10.1042/ebc20160087 · Cited by 12
Estimating kinetic mechanisms with prior knowledge II: Behavioral constraints and numerical tests
Navarro, M. A., Salari, A., Milescu, M., et al. (2018) · The Journal of General Physiology · doi:10.1085/jgp.201711912 · Cited by 13
“…solutions (theoretical parameter identifiability) or because the data are corrupted by noise and artifacts that flatten the cost function surface (practical parameter identifiability; Milescu et al., 2005; Raue et al., 2009; Siekmann et al., 2012; Hines et al., 2014; Middendorf and Aldrich, 2017).”
BackgroundStepien, T. L., Lynch, H. E., Yancey, S. X., Dempsey, L., & Davidson, L. A. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218021 · Cited by 14
“Estimating parameters for our model in a deterministic manner appeared infeasible as preliminary parameter space exploration hinted that our model had parameter structural nonidentifiability, or functionally related model parameters [48].”
MethodFAMoS: A Flexible and dynamic Algorithm for Model Selection to analyse complex systems dynamics
Gabel, M., Hohl, T., Imle, A., Fackler, O., & Graw, F. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007230 · Cited by 11
PDEparams: parameter fitting toolbox for partial differential equations in python
Parra-Rojas, C. A., & Hernandez-Vargas, E. A. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz938 · Cited by 13
Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release
Zitzmann, C., Kaderali, L., & Perelson, A. S. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008421 · Cited by 13
“In order to fit these models to data, global optimization was performed using the Data2Dynamics environment [32] for Matlab 2016b. Parameters were estimated by minimizing the https://doi.org/10.1371/journal.pcbi.1008421.t002 PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1008421 November 5, 2020 7 /…”
MethodInfluentialModel learning to identify systemic regulators of the peripheral circadian clock
Martinelli, J., Dulong, S., Li, X.-M., Teboul, M., Soliman, S., Lévi, F., Fages, F., & Ballesta, A. (2021) · Bioinformatics · doi:10.1093/bioinformatics/btab297 · Cited by 15
Dankwa, E. A., Donnelly, C. A., Brouwer, A. F., Zhao, R., Montgomery, M. P., Weng, M. K., & Martin, N. K. (2021) · Vaccine · doi:10.1016/j.vaccine.2021.10.001 · Cited by 16
González‐Parra, G., Díaz‐Rodríguez, M., & Arenas, A. J. (2022) · Spatial and Spatio-temporal Epidemiology · doi:10.1016/j.sste.2022.100532 · Cited by 13
Saha, J., Bose, P., Dhakal, S., Ghosh, P., & Rangachari, V. (2022) · Biochemistry · doi:10.1021/acs.biochem.2c00495 · Cited by 12
Ceballos‐Núñez, V., Richardson, A. D., & Sierra, C. A. (2018) · Biogeosciences · doi:10.5194/bg-15-1607-2018 · Cited by 12
Identification of parameters in systems biology
Abdulla, U. G., & Poteau, R. (2018) · Mathematical Biosciences · doi:10.1016/j.mbs.2018.09.004 · Cited by 13
Antibody-Mediated Immobilization of Virions in Mucus
Jensen, M. A., Wang, Y., Lai, S. K., et al. (2019) · Bulletin of Mathematical Biology · doi:10.1007/s11538-019-00653-6 · Cited by 13
Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
Simpson, M. J., Browning, A. P., Drovandi, C., Carr, E. J., Maclaren, O. J., & Baker, R. E. (2021) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2021.0214 · Cited by 14
“As such, a flat profile is indicative of non-identifiability, therefore a lack of information in the data about a parameter [10].”
BackgroundMethodInfluentialStochastic mathematical models for the spread of COVID-19: a novel epidemiological approach
Mourad, A., Mroue, F., & Taha, Z. (2021) · Mathematical Medicine and Biology A Journal of the IMA · doi:10.1093/imammb/dqab019 · Cited by 13
Estimating confidence intervals in predicted responses for oscillatory biological models
John, P. C. S., & Doyle, F. J. (2013) · BMC Systems Biology · doi:10.1186/1752-0509-7-71 · Cited by 13
“Practical identifiability analysis is concerned with calculating confidence intervals in parameter estimates resulting from uncertainty in experimental data [3].”
BackgroundNakagawa, S., Yang, Y., Macartney, E. L., Spake, R., & Lagisz, M. (2023) · doi:10.32942/x2kk5n · Cited by 13
Identifiability and experimental design in perturbation studies
Gross, T., & Blüthgen, N. (2020) · Bioinformatics · doi:10.1093/bioinformatics/btaa404 · Cited by 11
Muñoz‐Tamayo, R., & Tedeschi, L. O. (2023) · Journal of Animal Science · doi:10.1093/jas/skad320 · Cited by 15
“The profile likelihood approach (Murphy and Van Der Vaart, 2000; Raue et al., 2009) was applied to assess the practical identifiability of a model developed to describe the effect of diet composition on sheep weight (Vargas-Villamil et al., 2020).”
MethodKutumova, E. O., Akberdin, I. R., Egorova, V. S., Kolesova, E. P., Parodi, A., Pokrovsky, V. S., Zamyatnin, A. A., & Kolpakov, F. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e30962 · Cited by 12
Su, Z., Dong, C., Li, P., et al. (2016) · Infectious Disease Modelling · doi:10.1016/j.idm.2016.05.001 · Cited by 12
Fine-Tuning of Energy Levels Regulates SUC2 via a SNF1-Dependent Feedback Loop
Persson, S., Welkenhuysen, N., Shashkova, S., & Cvijović, M. (2020) · Frontiers in Physiology · doi:10.3389/fphys.2020.00954 · Cited by 13
“The method of profile likelihood (Raue et al., 2009), is typically superior to asymptotic approaches, such as FIM for investigating model identifiability.”
MethodModeling the spread of fake news on Twitter
Murayama, T., Wakamiya, S., Aramaki, E., & Kobayashi, R. (2021) · Institutional Repositories DataBase (IRDB) · Cited by 12
Geppert, J., Röse, P., Pauer, S., & Krewer, U. (2022) · ChemElectroChem · doi:10.1002/celc.202200481 · Cited by 12
Identifiable prediction animal model for the bi-hormonal intraperitoneal artificial pancreas
Benam, K. D., Khoshamadi, H., Åm, M. K., Stavdahl, Ø., Gros, S., & Fougner, A. L. (2022) · Journal of Process Control · doi:10.1016/j.jprocont.2022.11.008 · Cited by 11
Eberle, C., & Ament, C. (2011) · Biosystems · doi:10.1016/j.biosystems.2011.11.003 · Cited by 12
Hybrid Dynamic Optimization Methods for Systems Biology with Efficient Sensitivities
Lewis, N. R., Hedengren, J. D., & Haseltine, E. L. (2015) · Processes · doi:10.3390/pr3030701 · Cited by 12
“However, there is a unique challenge in systems biology, because there is often a combination of both large and unobservable models [18,19].”
BackgroundCombining test statistics and models in bootstrapped model rejection: it is a balancing act
Johansson, R., Strålfors, P., & Cedersund, G. (2014) · BMC Systems Biology · doi:10.1186/1752-0509-8-46 · Cited by 13
“Supplementary Figure S6: Effects of parameter uncertainty and sub-cloud realizations on p-value estimates.”
BackgroundInfluentialSchumacher, R., & Wahl, A. (2015) · Metabolites · doi:10.3390/metabo5040697 · Cited by 12
“Crucial for every modeling approach is sufficient information for the identification of the model parameters from the observables [20].”
BackgroundEstimability Analysis and Optimal Design in Dynamic Multi-scale Models of Cardiac Electrophysiology
Shotwell, M. S., & Gray, R. A. (2016) · Journal of Agricultural Biological and Environmental Statistics · doi:10.1007/s13253-016-0244-7 · Cited by 12
“This has generated interest in alternative criteria and tests for local identifiability (e.g., Hengl et al. 2007; Raue et al. 2009; Kim and Lindsay 2014).”
Nguyễn, V. K., & Hernandez-Vargas, E. A. (2015) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2015.12.135 · Cited by 12
The Physics behind Systems Biology
Radde, N. E., & Hütt, M. ‐. (2016) · EPJ Nonlinear Biomedical Physics · doi:10.1140/epjnbp/s40366-016-0034-8 · Cited by 15
“Examples consist of profile likelihoods [130], sampling-based Bayesian approaches, and, related to this, stochastic model approaches.”
BackgroundSequential Parameter Estimation for Mammalian Cell Model Based on In Silico Design of Experiments
Wang, Z., Sheikh, H., Lee, K., & Georgakis, C. (2018) · Processes · doi:10.3390/pr6080100 · Cited by 12
Santra, T. (2018) · Scientific Reports · doi:10.1038/s41598-018-30118-0 · Cited by 12
Havumaki, J., Meza, R., Phares, C. R., Date, K., & Eisenberg, M. C. (2019) · BMC Infectious Diseases · doi:10.1186/s12879-019-4688-6 · Cited by 12
Dynamical characterization of antiviral effects in COVID-19
Abuin, P., Anderson, A., Ferramosca, A., Hernandez-Vargas, E. A., & González, A. H. (2021) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2021.05.001 · Cited by 12
van Riel, N. A. W., Tiemann, C. A., Hilbers, P. A. J., & Groen, A. K. (2021) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2020.536957 · Cited by 12
Hierarchical Bayesian inference for ion channel screening dose-response data
Johnstone, R. H., Bardenet, R., Gavaghan, D. J., et al. (2017) · Wellcome Open Research · doi:10.12688/wellcomeopenres.9945.2 · Cited by 12
Brouwer, A. F., Eisenberg, M. C., Shulman, L. M., Famulare, M., Koopman, J. S., Kroiss, S. J., Hindiyeh, M. Y., Manor, Y., Grotto, I., & Eisenberg, J. N. S. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0006 · Cited by 12
Model-based translation of DNA damage signaling dynamics across cell types
Heldring, M. M., Wijaya, L. S., Niemeijer, M., Yang, H., Lakhal, T., Dévédec, S. E. L., van de Water, B., & Beltman, J. B. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010264 · Cited by 12
“In addition to Eqs 1–11, we used observable functions to map the state variables to the experimental observables, according to the method described in [47].”
MethodRanaee, E., Moghadasi, L., Inzoli, F., Riva, M., & Guadagnini, A. (2017) · Journal of Petroleum Science and Engineering · doi:10.1016/j.petrol.2017.09.062 · Cited by 12
“16 We assess here identifiability of model parameter i through its profile likelihood (PL), 17 ( )PL i , defined as (Raue et al., 2009) 18 2 ( ) ( ) min j i j PL i Y J”
MethodLeviyang, S., & Griva, I. (2018) · Viruses · doi:10.3390/v10100517 · Cited by 12
iVUN: interactive Visualization of Uncertain biochemical reaction Networks
Vehlow, C., Hasenauer, J., Kramer, A., Raue, A., Hug, S., Timmer, J., Radde, N., Theis, F. J., & Weiskopf, D. (2013) · BMC Bioinformatics · doi:10.1186/1471-2105-14-s19-s2 · Cited by 11
“file likelihoods based confidence intervals [38,39].”
Self-citationCassidy, T., Gillich, P., Humphries, A. R., et al. (2022) · IMA Journal of Applied Mathematics · doi:10.1093/imamat/hxac027 · Cited by 11
“This is convenient because ODE models are easy to implement in commonly used software packages for statistical inference [Carpenter et al., 2017], whereas support for DDE models is much less common, and often restricted to an Erlang distributed or fixed delay [Lixoft, 2019; Raue et al., 2014, 2009].”
MethodDisentangling ERBB Signaling in Breast Cancer Subtypes—A Model-Based Analysis
Kemmer, S., Berdiel‐Acer, M., Reinz, E., Sonntag, J., Tarade, N., Bernhardt, S., Fehling-Kaschek, M., Hasmann, M., Korf, U., Wiemann, S., et al. (2022) · Cancers · doi:10.3390/cancers14102379 · Cited by 11
“We therefore used the profile-likelihood method [43] obtaining confidence intervals for each parameter that were subsequently used for model reduction as described by Maiwald et al.”
MethodSelf-citationPrediction of microbial growth via the hyperconic neural network approach
Murrieta-Dueñas, R., Serrano-Rubio, J. P., López-Ramírez, V., et al. (2022) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2022.08.021 · Cited by 11
Zitzmann, C., Dächert, C., Schmid, B., van der Schaar, H. M., van Hemert, M. J., Perelson, A. S., van Kuppeveld, F. J. M., Bartenschlager, R. F. W., Binder, M., & Kaderali, L. (2023) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010423 · Cited by 12
Nguyen, K., Li, K., Flores, K., Tomaras, G. D., Dennison, S. M., & McCarthy, J. (2023) · Analytical Biochemistry · doi:10.1016/j.ab.2023.115263 · Cited by 12
Gnambs, T., & Schroeders, U. (2023) · Research Synthesis Methods · doi:10.1002/jrsm.1673 · Cited by 14
“Moreover, because RCT meta-analyses often include rather few primary studies with small samples, 33 the covariance in T 2 might be some-times practically non-identifiable, 34,35 thus, requiring modeling independent variances at pre-and posttest.”
BackgroundErdõs, B., O’Donovan, S. D., Adriaens, M. E., Gijbels, A., Trouwborst, I., Jardon, K. M. C., Goossens, G. H., Afman, L. A., Blaak, E. E., van Riel, N. A. W., et al. (2024) · Scientific Reports · doi:10.1038/s41598-024-58703-6 · Cited by 10
“We considered the combination of model and data as practically identifiable if the confidence interval of all estimated parameters were of finite size in the parameter scan range 39 .”
MethodLettermann, L., Jurado, A., Betz, T., Wörgötter, F., & Herzog, S. (2024) · Communications Physics · doi:10.1038/s42005-024-01606-9 · Cited by 12
Andreu‐Vilarroig, C., Villanueva, R. J., & González‐Parra, G. (2024) · Infectious Disease Modelling · doi:10.1016/j.idm.2024.04.006 · Cited by 11
Koopsen, T., van Osta, N., van Loon, T., et al. (2024) · BioMedical Engineering OnLine · doi:10.1186/s12938-024-01232-0 · Cited by 11
“Furthermore, we used diaphony as an index of identifiability, but other identifiability analysis methods have previously been described, such as profile likelihood analysis [27, 28].”
BackgroundMethodJain, P., Kizhuttil, R., Nair, M. B., Bhatia, S., Thompson, E. W., George, J. T., & Jolly, M. K. (2024) · iScience · doi:10.1016/j.isci.2024.110310 · Cited by 13
Rateitschak, K., Kaderali, L., Olaf Wolkenhauer, A., & Jaster, R. (2016) · Cellular Signalling · doi:10.1016/j.cellsig.2016.03.002 · Cited by 11
Sufficiently Exciting Inputs for Structurally Identifiable Systems Biology Models
Villaverde, A. F., Evans, N. D., Chappell, M. J., et al. (2018) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2018.09.015 · Cited by 11
“…is possible (for a given set of experiments with defined inputs) to assess identifiability with numerical approaches based on profile likelihoods (Raue et al., 2009) or the sensitivity matrix (Stigter and This project has received funding from the European Union’s Horizon 2020 research and…”
MethodInfluentialA diagnostic procedure for improving the structure of approximated kinetic models
Quaglio, M., Fraga, E. S., & Galvanin, F. (2019) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2019.106659 · Cited by 10
Metadata
- Authors
- Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., & Timmer, J.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Raue, A.
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2009-06-08
- Volume
- 25
- Issue
- 15
- Pages
- 1923-1929
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2168648059
- Cited by
- 1,442
- References
- 29
- Citations by year
- 2026: 209 · 2025: 107 · 2024: 103 · 2023: 82 · 2022: 98 · 2021: 118 · 2020: 97 · 2019: 116 · 2018: 94 · 2017: 78 · 2016: 87 · 2015: 64 · 2014: 52 · 2013: 54 · 2012: 39
- FWCI
- 10.99
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Bioinformatics (publishedVersion)
- PubMed (publishedVersion)
- OPUS (Augsburg University) (submittedVersion)
- Funders
- Deutsches Krebsforschungszentrum
- European Commission (223188, EU-FP7, FP7 HEALTH)
- Bundesministerium für Bildung und Forschung (FRISYS 0313921, 0313074D, 0313921)
- FP7 Health
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Microbial Metabolic Engineering and Bioproduction
- Keywords
- identifiability analysis, profile likelihood, parameter estimation, confidence intervals, experimental design, model reduction
- MeSH terms
- Algorithms, Models, Biological, Probability, Computational Biology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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