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Identifiability and observability analysis for experimental design in nonlinear dynamical models
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Image of FIG. 1.
FIG. 1.
Image of FIG. 2.
FIG. 2.

Model for ligand binding as well as EpoR and ligand trafficking. The dashed boxes correspond to the quantities accessible by measurement of radioactively labeled ligand.

Image of FIG. 3.
FIG. 3.

The profile likelihood of the model parameters are displayed in combination with the thresholds yielding with confidence intervals that hold for each parameter individually. The optimal parameter value is indicated by an asterisk, if unique. (a) The flatness of the profile likelihood reveals that five parameters are structurally nonidentifiable, given the initial setup. (b) By including information about the initial Epo concentration, the structural nonidentifiability can be resolved. Parameter remains practically nonidentifiable. (c) By including measurements of intracellular Epo, all parameters are structurally and practically identifiable.

Image of FIG. 4.
FIG. 4.

Initial setup: the change of the other parameters along the profile likelihood indicates functional relations between all five structural nonidentifiable parameter, indicated by the solid lines.

Image of FIG. 5.
FIG. 5.

The figure shows dependency of the trajectories of the model observable and of species concentration on uncertainties in the parameter estimates. (a) The concerted change of parameters along the structural nonidentifiability of (see Fig. 4) does not affect the model observables but shift the trajectories of species concentration by a common factor. (b) The practical nonidentifiability of only slightly affects the model observables , staying in agreement with the measurement precision of the experimental data. Nevertheless, the trajectories of species EpoR, Epo_EpoR_i, and dEpo_i are affected. (c) The remaining uncertainties in the identifiable parameters, as displayed in Fig. 3(c), translate to confidence intervals of the model trajectories.

Image of FIG. 6.
FIG. 6.

The appropriateness of confidence intervals was assessed by a simulation study with 450 generated data sets. (a) Comparison of the amount of overfitting to the expected distribution with . (b) The solid lines indicate the CRs for the time pointwise confidence bands on the model trajectories shown in Fig. 5(c). The dashed lines are the desired 95% level of confidence, while the gray shades are the expected coverage rates.


Generic image for table
Table I.

Individual confidence intervals of the model parameter to a confidence level of 95%. Values are given on a scale. The CRs of the estimates are in line with the expected values (93.33% and 96.66%).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Identifiability and observability analysis for experimental design in nonlinear dynamical models