The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index; 1 of the 12 sources its claims cite were checked for support.
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.
Overview
AI snapshot
Written from the paper’s full text.
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.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
1 of 12 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
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.
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
“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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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.
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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 14
- Probably not a substantial claim. 13
The cited sources support only part of this claim — read each source’s verdict below.
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)
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Partly supported
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The 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
“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
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Not matched
None of the sources cited for this claim have been checked yet.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“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 > )]:
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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 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
Strength:plain· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
- Also stated in: § 6 DISCUSSION · plain
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 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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence.
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
“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
Strength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
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 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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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
Cites
Press, W. H., Teukolsky, S. L. A., Flannery, B. P., & Vetterling, W. T. (1990) · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · Cited by 6,980
Ziegel, E. R., Lehmann, E. L., & Casella, G. (1999) · Technometrics · doi:10.2307/1270597 · Cited by 4,203
Lehmann, E. L. (1983) · Springer eBooks · doi:10.1007/978-1-4757-2769-2 · Cited by 1,357
Murphy, S. A., & Van Der Vaart, A. W. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474219 · Cited by 712
On global identifiability for arbitrary model parametrizations
Lennart Ljung, A., & Glad, T. (1994) · Automatica · doi:10.1016/0005-1098(94)90029-9 · Cited by 644
A method for computing profile-likelihood-based confidence intervals
Venzon, D. J., & Moolgavkar, S. H. (1988) · Applied Statistics · doi:10.2307/2347496 · Cited by 565
Systems biology toolbox for matlab: a computational platform for research in systems biology
Schmidt, H., & Jirstrand, M. (2006) · Bioinformatics · doi:10.1093/bioinformatics/bti799 · Cited by 473
System identifiability based on the power series expansion of the solution
Pohjanpalo, H. (1978) · Mathematical Biosciences · doi:10.1016/0025-5564(78)90063-9 · Cited by 440
Parameter and structural identifiability concepts and ambiguities: a critical review and analysis
Cobelli, C., & DiStefano, J. J. (1980) · American Journal of Physiology-Regulatory, Integrative and Comparative Physiology · doi:10.1152/ajpregu.1980.239.1.r7 · Cited by 402
Swameye, I., Müller, T. G., Timmer, J., Sandra, O., & Klingmüller, U. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0237333100 · Cited by 316
Self-citation
Flagged first, then by citations
1 of the 29 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Items 901–1,000 of 1,414
Rong, Y., Qin, C., Yen, H., et al. (2024) · Journal of Environmental Management · doi:10.1016/j.jenvman.2023.119955 · Cited by 3
Tsiros, P., Minadakis, V., Li, D., & Sarimveis, H. (2024) · Toxicological Sciences · doi:10.1093/toxsci/kfae051 · Cited by 5
“This is because complex models are prone to parameter identifiability issues, causing them to lose their mechanistic nature (Garcia et al. , 2015; Peters and Dolgos, 2019; Raue et al. , 2009; Slob et al. , 1997; Yates, 2006).”
Backgroundvan Noort, M., & Ruppert, M. (2024) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.13147 · Cited by 3
Han, Y., & Styczynski, M. P. (2024) · npj Systems Biology and Applications · doi:10.1038/s41540-024-00412-x · Cited by 5
Employing Observability Rank Conditions for Taking into Account Experimental Information a priori
Villaverde, A. F. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01415-3 · Cited by 3
A new method for a priori practical identifiability
Thompson, P. E., Andersson, B. J., Sundqvist, N., & Cedersund, G. (2025) · PLoS ONE · doi:10.1371/journal.pone.0327593 · Cited by 3
Evaluation of pharmacokinetic model designs for subcutaneous infusion of insulin aspart
Mansell, E. J., Schmidt, S., Docherty, P. D., Nørgaard, K., Jørgensen, J. B., & Madsen, H. (2017) · Journal of Pharmacokinetics and Pharmacodynamics · doi:10.1007/s10928-017-9535-z · Cited by 3
“Practical identifiability analyses ultimately determine whether there is significant distinguishability between model parameters [15, 16, 23]; in contrast, a priori or structural identifiability analyses require only infinitesimal distinguishability between model parameters to declare a model identifiable [26–28].”
BackgroundDas, J., & Lanier, L. L. (2019) · Journal of Leukocyte Biology · doi:10.1002/jlb.6mr1218-505r · Cited by 3
Derivation and identification of a mechanistic model for a branched enzyme‐catalyzed carboligation
Ohs, R., Fischer, K., Schöpping, M., & Spieß, A. C. (2019) · Biotechnology Progress · doi:10.1002/btpr.2868 · Cited by 3
“In contrast to structural identifiability, practical identifiability also takes the amount and quality of measured data, which was used for parameter calibration, into account.(47) To test practical identifiability, we generated progress curve data in silico using assumed parameter values.”
BackgroundMethodLeveraging Resource Competition for Part Characterization in Cell-Free Extracts
György, A. (2019) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2019.12.230 · Cited by 3
Lai, X., Keller, C., Santos, G., Schaft, N., Dörrie, J., & Vera, J. (2022) · Frontiers in Cell and Developmental Biology · doi:10.3389/fcell.2021.746359 · Cited by 3
“This is due to the relatively small number of experimental data that are available for parameter estimation (Raue et al., 2009).”
BackgroundGürkan-Çavusoglu, E., Schupp, J. E., Kinsella, T. J., & Loparo, K. A. (2013) · IET Systems Biology · doi:10.1049/iet-syb.2012.0050 · Cited by 3
Teergele, J., & Danai, K. (2014) · International Journal of Systems Science · doi:10.1080/00207721.2014.884251 · Cited by 3
“…and/or external stimuli (Mehra, 1974; Thomaseth & Cobelli, 1999); and (3) practical identifiabil-ity to further account for the quality of observations and the ability to estimate unique model parameters from the actual observations (Hengl, Kreutz, Timmer, & Maiwald, 2007; Raue et al., 2009).”
BackgroundStatistical method for estimation of the predictive power of a gene circuit model
Myasnikova, E. M., & Kozlov, K. N. (2014) · Journal of Bioinformatics and Computational Biology · doi:10.1142/s0219720014410029 · Cited by 3
XI, F., CHEN, S., & LIU, Z. (2013) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127413501988 · Cited by 3
“The topic of the parameter identifiability is well established in mathematical modeling within science and engineering [Jacquez & Greif, 1985; Zak et al., 2003; Rodriguez-Fernandez et al., 2006; Raue et al., 2009].”
BackgroundJohansson, R. (2017) · Linköping studies in science and technology. Dissertations · doi:10.3384/diss.diva-141614 · Cited by 4
Direct continuous-time parameter identification of excitation system with the generator online
Kian, M., Najafabadi, T. A., Lesani, H., et al. (2018) · IEEE Texas Power and Energy Conference (TPEC) · doi:10.1109/tpec.2018.8312058 · Cited by 3
“On the other hand, identifiability analysis should be performed to evaluate the precision of model parameters obtained by the estimation method [18].”
MethodBand, L. R., & Preston, S. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.05.028 · Cited by 3
Sensitivity Analysis for Global Parameter Identification. Application to Aerodynamic Coefficients
Albisser, M., & Dobre, S. (2018) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2018.09.069 · Cited by 3
Geometrically Motivated Reparameterization for Identifiability Analysis in Power Systems Models
Transtrum, M. K., Francis, B. L., Youn, C. C., et al. (2018) · North American Power Symposium (NAPS) · doi:10.1109/naps.2018.8600617 · Cited by 3
“In contrast to structural identifiability, there is no universally accepted definition of practical identifiability [8], [9].”
BackgroundOn the Use of Online Reparametrization in Automated Platforms for Kinetic Model Identification
Quaglio, M., Waldron, C. J., Pankajakshan, A., et al. (2019) · Chemie Ingenieur Technik · doi:10.1002/cite.201800095 · Cited by 3
Model-based small area estimation at two scales using Moran's spatial filtering
Truong, P. N., & Stein, A. A. (2019) · Spatial and Spatio-temporal Epidemiology · doi:10.1016/j.sste.2019.100303 · Cited by 3
Динаміка перехідних процесів у незворотних кінетичних моделях
Teslenko, V. I., & Kapitanchuk, O. L. (2012) · Ukrainian Journal of Physics · doi:10.15407/ujpe57.5.573 · Cited by 3
Mathematical Modelling of Cell Culture Processes
Chotteau, V., Hagrot, E., Zhang, L., & Mäkinen, M. (2021) · Cell engineering · doi:10.1007/978-3-030-79871-0_14 · Cited by 4
Determining Structurally Identifiable Parameter Combinations Using Subset ProfilingPreprint
Eisenberg, M. C., & Hayashi, M. A. L. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1307.2298 · Cited by 3
OBTAINING THE BEST MODEL PREDICTIONS AND PARAMETER ESTIMATES USING LIMITED DATA
McLean, K. A. P. (2011) · QSpace (Queen's University Library) · Cited by 3
Constructing Predictive Cancer Systems Biology ModelsPreprint
Rohrs, J. A., Makaryan, S. Z., & Finley, S. D. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/360800 · Cited by 3
Elements of asymptotic theory with outer probability measuresPreprint
Houssineau, J., Chada, N. K., & Delande, E. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1908.04331 · Cited by 3
Multidimensional single-cell modeling of cellular signalingPreprint
Wade, J. D., Lun, X., Bodenmiller, B., & Voit, E. O. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.11.15.383711 · Cited by 3
Oderbolz, J., Zangger, N. S., Zimmermann, L., Sandu, I., Starruß, J., Graw, F., & Oxenius, A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.01.14.426650 · Cited by 3
Untangling the cell immune response dynamic for severe and critical cases of SARS-CoV-2 infectionPreprint
Blanco‐Rodríguez, R., Du, X., & Hernandez-Vargas, E. A. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.03.23.436686 · Cited by 3
“Here we 135 used the profile likelihood method proposed by [35].”
MethodShin, S., Chew, N. J., Ghomlaghi, M., Chüeh, A. C., Jeong, Y., Nguyen, L. K., & Daly, R. J. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.11.03.467180 · Cited by 3
Efficient Inference on a Network of Spiking Neurons using Deep LearningPreprint
Baldy, N., Breyton, M., Woodman, M., Jirsa, V., & Hashemi, M. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.01.26.577077 · Cited by 3
Active learning maps the emergent dynamics of enzymatic reaction networks.Preprint
Jakštaitė, ., Zhou, T., Nelissen, F. H. T., Huck, W. T. S., & van Sluijs, B. (2024) · ChemRxiv · doi:10.26434/chemrxiv-2024-vxfkz · Cited by 2
Identifiability-Guided Assessment of Digital Twins in Alzheimer’s Disease Clinical Research and CarePreprint
Jiang, J., Petrella, J. R., Hao, W., & Initiative, T. A. D. N. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.08.17.670697 · Cited by 3
“Even identifiable parameters yield estimates accompanied by uncertainty, typically expressed as confidence intervals that quantify the probable range of true parameter values 27 .”
InfluentialFLAT LIKELIHOODS: BINOMIAL CASE
Montoya, J. A. (2022) · Revista de la Facultad de Ciencias · doi:10.15446/rev.fac.cienc.v11n2.97888 · Cited by 2
Identifying Bayesian optimal experiments for uncertain biochemical pathway models
Isenberg, N. M., Mertins, S. D., Yoon, B.-J., Reyes, K. G., & Urban, N. M. (2024) · Scientific Reports · doi:10.1038/s41598-024-65196-w · Cited by 3
“Furthermore, the framework we lay out here is general and applicable to any relevant biological modeling setting where experimental data is obtainable.”
Reducing Structural Nonidentifiabilities in Upstream Bioprocess Models Using Profile‐Likelihood
Babel, H., Omar, O., Paul, A. J., & Bär, J. W. (2025) · Biotechnology and Bioengineering · doi:10.1002/bit.28922 · Cited by 2
“Consequently, there are functional relations h between the redundant parameters θ sub (Raue et al. 2009).”
InfluentialWang, R., Weber, Z. M., Janik, M. J., et al. (2025) · ACS Catalysis · doi:10.1021/acscatal.4c05157 · Cited by 2
Pashapour, M., Abbaszadeh, M., & Dehghan, M. (2025) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-025-06220-4 · Cited by 4
Zhao, S., Keller, E. T., Robinson, T., et al. (2025) · npj Systems Biology and Applications · doi:10.1038/s41540-025-00540-y · Cited by 2
On the inferential consequences in the selection of fractional derivatives
Caraveo-Balderas, L. A., Laos, J. A. M., & Ramírez-Ramírez, L. L. (2025) · Applied Mathematical Modelling · doi:10.1016/j.apm.2025.116386 · Cited by 2
A Markov Chain Monte Carlo Procedure for Efficient Bayesian Inference on the Phase-Type Aging Model
Nie, C., Liu, X., Provost, S. B., et al. (2025) · Stats · doi:10.3390/stats8030077 · Cited by 2
“The estimability issue arising from flat profile likelihood functions is thoroughly discussed in [3].”
Dorešić, D., Pathirana, D., Weindl, D., & Hasenauer, J. (2025) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2025.100558 · Cited by 2
Power loss model identification in gearboxes: Balancing identifiability and testing time
Fard, A. M. Z., Rottiers, W., Kirchner, M., et al. (2025) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2025.106224 · Cited by 2
Blanco‐Rodríguez, R., Miura, T. A., & Hernandez-Vargas, E. A. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1013704 · Cited by 2
“A computational technique employing profile likelihood was introduced by Raue et al. [4] to determine model parameters in ordinary differential equations based on experimental data.”
InfluentialA Cautionary Tale of Model Misspecification and Identifiability
Browning, A. P., Flegg, J. A., & Murphy, R. J. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01573-4 · Cited by 2
“Typical suggestions in the literature are model reduction, reparameterisation, or simplification [7]; to increase the quantity or quality of data [9]; or to modify the type of measurements that can be observed (for example, to additionally (1) with β = 2) with a range of initial conditions u (0) =…”
From big data to mechanistic insights: decoding plant complexity with models
Politsch, J. E., González-Delgado, A., & Wabnik, K. (2026) · Current Opinion in Biotechnology · doi:10.1016/j.copbio.2025.103428 · Cited by 3
A Nonparametric Approach to Practical Identifiability of Nonlinear Mixed Effects Models
Cassidy, T., Johnston, S. T., Plank, M., Botha, I., Flegg, J. A., Murphy, R. J., & Hamis, S. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01583-2 · Cited by 3
“Consequently, several analytic and computational approaches have been developed to study the iden-tifiability of a mathematical model (Dong et al. 2023; Raue et al. 2009; Maiwald et al. 2016; Sharp et al. 2022; Ciocanel et al. 2024; Bellu et al. 2007; Raue et al. 2014; Stapor et al. 2018).”
Influentialvon Boros, L., Schaubruch, L. M., Arnold, M., Rigotti, T., Helmreich, I., Lieb, K., Wessa, M., Tüscher, O., & Schäfer, S. K. (2026) · Work & Stress · doi:10.1080/02678373.2026.2618071 · Cited by 2
“Model fit and parameterisation were examined by visual inspection of log-likelihood profiles, which were supposed to show single peaks (Raue et al., 2009; Viechtbauer, 2010).”
Chen, G., Korolija, I., & Rovas, D. (2026) · Energy and Buildings · doi:10.1016/j.enbuild.2026.117139 · Cited by 3
Daher, A., Trucu, D., & Eftimie, R. (2026) · npj Systems Biology and Applications · doi:10.1038/s41540-026-00657-8 · Cited by 2
Shao, W., Liu, L., Qu, X., et al. (2026) · Energy Conversion and Management · doi:10.1016/j.enconman.2026.121589 · Cited by 2
Grey-box modeling framework for consolidated bioprocessing systems: an endpoint-guided approach
Yeboah, M. K., & Söffker, D. (2026) · Bioresources and Bioprocessing · doi:10.1186/s40643-026-01101-9 · Cited by 2
“Future work should include identifiability analysis, Bayesian or multi-start parameter estimation, and explicit oxygen dynamics when suitable measurements become available (Mahanty 2023; Wang et al. 2023; Raue et al. 2009).”
Spoto, S. E. (2026) · Soil Systems · doi:10.3390/soilsystems10080093 · Cited by 2
Elsheikh, A. M. G. (2013) · EUROSIM Congress on Modelling and Simulation (EUROSIM) · doi:10.1109/eurosim.2013.61 · Cited by 2
“practical IA, see [3] for more formal details.”
BackgroundIdentifiability Analysis of Load Model Parameter Identification with Likelihood Profile Method
Zhang, X., Lü, C., & Wang, Y. (2018) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm.2018.8586673 · Cited by 2
“In the area of power system, the identifiability of generator parameter has been analyzed in [10] using the same likelihood profile method as in [7].”
MethodEstimating chain length for time delays in dynamical systems using profile likelihood
Hauber, A. L., Engesser, R., Vanlier, J., & Timmer, J. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz838 · Cited by 2
Self-citationLi, Y., Lee, H., Heo, W. D., & Zi, Z. (2021) · Advanced Biology · doi:10.1002/adbi.202101008 · Cited by 2
Eudy‐Byrne, R. J., Riggs, M. M., Hawi, A. A., Sciascia, T. R., & Rohatagi, S. (2023) · British Journal of Clinical Pharmacology · doi:10.1111/bcp.15663 · Cited by 2
Sharma, S., Gowda, P., Lathoria, K., Mitra, M. K., & Sen, E. (2023) · Integrative Biology · doi:10.1093/intbio/zyad008 · Cited by 2
Mathematical Modeling of Toxoplasmosis in Cats with Two Time Delays under Environmental Effects
Sultana, S., González‐Parra, G., & Arenas, A. J. (2023) · Mathematics · doi:10.3390/math11163463 · Cited by 2
Dimitriou, N. M., Demirag, E., Strati, K., & Mitsis, G. D. (2023) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2023.107920 · Cited by 2
Lam, N. N., Murray, R., & Docherty, P. D. (2024) · Bulletin of Mathematical Biology · doi:10.1007/s11538-024-01304-1 · Cited by 3
“…as measurement noise and discrete sampling locations can restrict the information available for the process of parameter identification, potentially leading to practical identifiability issues (Raue et al. 2009; Hines et al. 2014; Wieland et al. 2021; Lam et al. 2022; Muñoz-Tamayo and Tedeschi 2023).”
BackgroundMethodInfluentialCadot, S., Audebert, C., Dion, C., Ken, S., Dupré, L., Largeaud, L., Laurent, C., Ysebaert, L., Crauste, F., & Quillet‐Mary, A. (2024) · PLoS Medicine · doi:10.1371/journal.pmed.1004430 · Cited by 2
Bakshi, A., Sengupta, S., De, R. K., & Dasgupta, A. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.125339 · Cited by 2
Ten quick tips to get you started with Bayesian statistics
Giménez, O., Royle, A., Kéry, M., & Nater, C. R. (2025) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1012898 · Cited by 3
“In addition, you should consider reparameterizing your model [26–28].”
Peloquin, J. M., & Elliott, D. M. (2024) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0415 · Cited by 2
Modeling the Differential Effect of CYP2C9 Gene Alleles on Losartan Metabolism
Babaev, D. S., Kutumova, E. O., & Kolpakov, F. (2024) · Mathematical Biology and Bioinformatics · doi:10.17537/2024.19.533 · Cited by 2
Challenges in the mathematical modeling of the spatial diffusion of SARS-CoV-2 in Chile
González‐Parra, G., Pérez, C.-L., Llamazares, M., Villanueva, R. J., Villegas-Villanueva, J., & Instituto de Matemática Multidisciplinar, U. P. D. V. (2025) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2025062 · Cited by 2
“More complex calibration processes can be implemented by for instance leaving the di ff usion coe ffi cients as parameters to be estimated, but the identifiability of the model would not be guaranteed [92].”
Zhao, Y., Averga, S., Buonomo, B., & Lou, J. (2025) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2025.112280 · Cited by 3
Mathematical and Computational Nuclear Oncology
Ryhiner, M., Song, Y., Saboury, B., Glatting, G., Rahmim, A., & Shi, K. (2025) · PET Clinics · doi:10.1016/j.cpet.2025.09.005 · Cited by 4
“To ensure robust parameter estimation and prevent overfitting, structural and practical identifiability analyses are performed, particularly for highly parametrized models with limited clinical time-point data 118 .”
Methodology to Perform Identifiability Analysis for Off-Road Vehicle Tire-Soil Parameter Estimation
Nielsen, S. L., Karkee, M., & Steward, B. L. (2011) · 2011 Louisville, Kentucky, August 7 - August 10, 2011 · doi:10.13031/2013.38126 · Cited by 2
“Raue et al. (2009) and (2011) described a numerical approach to local structural and practical identifiability based on the profile likelihood of the model parameters.”
BackgroundMethodInfluentialVillaverde, A. F., & Banga, J. R. (2019) · Jornadas de Automática · doi:10.17979/spudc.9788497497169.631 · Cited by 2
“En [3] se analizó numéricamente la identificabilidad de los parámetros del modelo usando el método del “profile likelihood” [18], concluyendo que seis de ellos (θ5 ≡ CISRNATurn, θ8 ≡ EpoRCISInh, θ11 ≡ JAK2EpoRDeaSHP1, θ12 ≡ SHP1ActEpoR, θ18 ≡ SOCS3RNADelay y θ20 ≡ SOCS3Turn) son prácticamente no identificables.”
Global fitting and parameter identifiability for amyloid-β aggregation with competing pathways
Rana, P., Bose, P., Vaidya, A., Rangachari, V., & Ghosh, P. (2020) · IEEE International Conference on Bioinformatics and Bioengineering (BIBE) · doi:10.1109/bibe50027.2020.00020 · Cited by 2
Dahlquist, E. (2019) · Linköping electronic conference proceedings · doi:10.3384/ecp20170 · Cited by 2
Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra
Haffke, B., Möller, R., Melz, T., et al. (2015) · Mathematical Problems in Engineering · doi:10.1155/2015/793216 · Cited by 2
“There are two phenomena which could account for the parameters to be nonidentifiable: structural nonidentifiability and practical nonidentifiability [16].”
BackgroundSaccomani, M. P. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-16483-0_63 · Cited by 2
Incorporating bolus and infusion pharmacokinetics into the ICING insulin model
Fisk, L., Docherty, P. D., Pretty, C. G., & Chase, J. G. (2016) · Mathematical Biosciences · doi:10.1016/j.mbs.2016.08.005 · Cited by 2
Testing the Pattern of AKT Activation by Variational Parameter Estimation
Kaschek, D., Henjes, F., Hasmann, M., et al. (2016) · IEEE Life Sciences Letters · doi:10.1109/lls.2016.2615081 · Cited by 2
“On the other hand, maximum-likelihood estimation and likelihood theory provide a solid statistical framework for uncertainty analysis [8], identifiability analysis [9], and model selection [10].”
MethodSelf-citationStructural Identifiability Analysis of Steady-State Induction Machine Models
Alturas, A. M., Gadoue, S. M., Elgendy, M. A., Zahawi, B., & Abdel-Khalik, A. S. (2015) · International Conference on Electric Power and Energy Conversion Systems · doi:10.1109/epecs.2015.7368508 · Cited by 2
Yang, H., Meijer, H. G. E., Buitenweg, J. R., & van Gils, S. A. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.01884 · Cited by 2
“, nP} and nP is the number of parameters (Raue et al., 2009).”
BackgroundMethodInfluentialDerivation and Use of Mathematical Models in Systems Biology
Smith, R. W., & Fleck, C. (2017) · Springer eBooks · doi:10.1007/978-3-319-56645-0_13 · Cited by 2
Estimation of lung absorption parameters for oxides of 238 Pu
Gregoratto, D., & Bailey, M. R. (2018) · Journal of Radiological Protection · doi:10.1088/1361-6498/aac19d · Cited by 2
“indicates that the parameter pi is identifiable, while a profile that is entirely flat or that tails out to a plateau on one side only, indicates that the parameter pi is not identifiable or that only a lower or upper limit can be determined from the data [21] .”
BackgroundMethodISAP-MATLAB Package for Sensitivity Analysis of High-Dimensional Stochastic Chemical Networks
Hu, W., Pantazis, Y., & Katsoulakis, M. A. (2018) · Journal of Statistical Software · doi:10.18637/jss.v085.i03 · Cited by 2
“Package PottersWheel introduced mean optimal transformations (Hengl, Kreutz, Timmer, and Maiwald 2007), a non- parametric bootstrap-based algorithm, and the profile likelihood (Raue et al. 2009) method for sensitivity analysis.”
MethodZen and the art of parameter estimation in systems biology
Myers, C. R. (2018) · CRC Press eBooks · doi:10.1201/9781315119847-8 · Cited by 4
“examined this same model in their use of the profile likelihood to analyze structural and practical parameter identifiability [21].”
MethodOptimal parameter identification of synthetic gene networks using harmony search algorithm
Zhang, W., Li, W., Zhang, J., & Wang, N. (2019) · PLoS ONE · doi:10.1371/journal.pone.0213977 · Cited by 2
Robust calibration of hierarchical population models for heterogeneous cell populations
Loos, C., & Hasenauer, J. (2019) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2019.110118 · Cited by 2
Bertrams, W., Jung, A. L., & Schmeck, B. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-801238-3.11689-7 · Cited by 2
Lam, N. N., Murray, R., Docherty, P. D., Morenga, L. T., & Chase, J. G. (2021) · Journal of Diabetes Science and Technology · doi:10.1177/19322968211021602 · Cited by 2
Salaberría, F., Delpino, C., Palla, C. A., et al. (2021) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2021.08.016 · Cited by 2
Degasperi, A., Nguyen, L. K., Fey, D., et al. (2021) · Methods in molecular biology · doi:10.1007/978-1-0716-1767-0_5 · Cited by 2
Using mathematical modeling to estimate time-independent cancer chemotherapy efficacy parameters
Pho, C., Frieler, M., Akkaraju, G. R., Naumov, A. V., & Dobrovolny, H. M. (2021) · In Silico Pharmacology · doi:10.1007/s40203-021-00117-7 · Cited by 2
“With the exception of that one estimate of max , the profiles indicate that there is at least local identifiability of the parameters (Raue et al. 2009).”
BackgroundMathematical Modelling in Plant Synthetic Biology
Deneer, A., & Fleck, C. C. (2022) · Methods in molecular biology · doi:10.1007/978-1-0716-1791-5_13 · Cited by 2
Schmitt, T., & Ritter, B. (2020) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2020.12.1312 · Cited by 4
Volpatto, D., Resende, A. C. M., dos Anjos, L., et al. (2022) · Trends in Computational and Applied Mathematics · doi:10.5540/tcam.2022.023.02.00223 · Cited by 2
Hu, J., Mei, Y., Holte, S., et al. (2022) · Journal of Applied Statistics · doi:10.1080/02664763.2022.2117288 · Cited by 2
Bayesian Inference for Thermal Model of Synchronous Generator—Part I: Parameter Estimation
Pandey, M., & Lie, B. (2022) · IEEE Access · doi:10.1109/access.2022.3209232 · Cited by 2
Models of vimentin organization under actin-driven transport
Park, Y., Leduc, C., Etienne‐Manneville, S., & Portet, S. (2023) · Physical review. E · doi:10.1103/physreve.107.054408 · Cited by 2
The Identifiability of Mathematical Models in Epidemiology: Tuberculosis, HIV, COVID-19
Игоревна, К. О., Kabanikhin, S. I., & Petrakova, V. (2023) · Mathematical Biology and Bioinformatics · doi:10.17537/2023.18.177 · Cited by 3
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.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
