Identifiability Analysis

Consider a parameter pj in a model for which a particular data set, ZN, has been collected. Loosely speaking, this parameter is identifiable with respect to the data if the data set contains sufficient information to uniquely determine the parameter. It is common to distinguish between two levels of identifiability structural and 

Structural Identifiability If pj is structurally identifiable it can, in principle, be estimated from the type of data present in ZN, if the data were perfect . One does therefore not take the practical limitations of the data into account Such limitations include for instance the noise level, the type of excitation of the system, the actual number of samples, and the sample distance. Likewise, one does not take into account the practical limitations associated with the optimization. Structural identifiability is therefore a necessary, but not sufficient, requirement for practical identifiability. Finally, structural identifiability may be treated with differential algebra, and an implementation that performs the calculations in a reasonable time, although with the cost of probabilistic results, has been provided by Sedoglavic [31, 32], 

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TABLE 23 Procedure for Identifying Analysis of Covariance Model... 

With regards to the analysis of the quality of the various parts of the model, one may use the same methods as are used for practical identifiability analysis. Since the same methods are used, albeit with different objectives, one sometimes refers to this model quality analysis as a posteriori identifiability (and the previous analysis as a priori identifiability). Now, however, one is also interested in how the parametric uncertainty translates to an uncertainty in the various model predictions. For instance, it might be so that even though two individual parameters have a high uncertainty, they are correlated in such a manner that their effect on a specific (non-measured) model output is always the same. Such a translation may be obtained by simulations of the model using parameters within the determined confidence ellipsoids. A global alternative to this is to consider the outputs for all parameters that correspond to a cost function that is below a certain threshold, for example 2% above the found minimum. 

Doyle and co-workers have used sensitivity and identifiability analyses in a complex genetic regulatory network to determine practically identifiable parameters (Zak et al., 2003), i.e., parameters that can be extracted from experiments with a certain confidence interval, e.g., 95%. The data used for analyses were based on simulation of their genetic network. Different perturbations (e.g., step, pulse) were exploited, and an identifiability analysis was performed. An important outcome of their analysis is that the best type of perturbations for maximizing the information content from hybrid multiscale simulations differs from that of the deterministic, continuum counterpart model. The implication of this interesting finding is that noise may play a role in systems-level tasks. 

IDENT2 and IDENT3 are provided as FORTRAN source code (IDENT2C is provided in C) for VAX VMS and other systems. It performs identifiability analysis. 

Figure 1.18 Indistinguishable parent-metabolite models for isoniazid. Parent drug is administered into Compartment 1 with parent and metabolite concentrations measured in Compartment 1 and 2, respectively. The models in the first column are pairwise symmetric to those in the second column by interchanging Compartments 2 and 4. The same is true for the third and fourth columns. All 18 of these models are kinetically indistinguishability and identifiable. Reprinted from Mathematical Biosciences, vol. 103, Zhang L-Q, Collins KC, and King PH Indistinguishability and identifiability analysis of linear compartmental models, pp. 77-95. Copyright (1971) with permission of Elsevier.

Evans, N.D., Godfrey, K.R., Chapman, M.J., Chappell, M.J., Aarons, L., and Duffull, S. An identifiability analysis of parent-metabolite pharmacokinetic model for ivabradine. Journal of Pharmacokinetics and Pharmacodynamics 2001 28 93-105. 

Zhang, L.-Q., Collins, J.C., and King, P.H. Indistinguishabil-ity and identifiability analysis of linear compartmental models. Mathematical Biosciences 1991 103 77-95. 

Brun, R., Reichert, P. and Kunsch, H.R. (2001) Practical identifiability analysis of large environmental simulation models. Water Resources Research 37, 1015-1030. 

Vajda, S., Godfrey, K. R., and Rabitz, H. (1989). Similarity transformation approach to identifiability analysis of nonlinear compartmental models. Math. Biosci 93,217-248. Walter, E. (1982). Identifiability of State Space Models, Lect. Notes Biomath. No. 46. Springer-Verlag, New York... 

As with HPLC, there will be no universal CE conditions that will be appropriate for the analysis of all types of samples/analytes. In fact, it has been shown that one set of conditions is not sufficient for the analysis of one class of proteins, for example, glycoproteins, or even variants of the same proteins from different species. One of the first steps in designing a method is to determine, on the basis of the type or class of analyte involved, which of the CE modes is best suited to the sample (Table 1.2). Once the appropriate CE mode has been identified, analysis is carried out and separation optimization initiated. Optimal separation of the components of any sample requires a logical approach to sample solubilization and/or dealing with diverse sample matrices as well as identification and utilization of the correct combination of CE operating parameters. Each of these will have distinct effects on the resultant separation and resolution. There is a massive literature on... 

Each case discussion begins with presentation of the basic facts of the situation and, where needed, critical historical background. Next, one or more ethical issue(s) raised in the case is identified. Analysis of the identified issue(s) then follows, with attention to, among other things, how the FEREs apply to the specific situation under scrutiny. Each case study concludes with discussion of one or more lesson(s) that the case suggests, often ones whose appUcabiUty extends far beyond the case at hand. 

Computing needs are described in the EUROCOMP Handbook. Some identified analysis and design capabilities are useful but not necessary in the design of conventional composite structures. 

All accidents and near-miss incidents should be investigated to determine causes, and means for their prevention identified. Analysis of injury and illness trends over time should be undertaken so that patterns with common causes can be identified and prevented. 

Boens N, Novikov E, Ameloot M (2006) Compartmental modeling of the fluorescence anisotropy decay of a cylindrically symmetric Brownian rotor identifiability analysis. Chemphyschem 7(12) 2559-2566. doi 10.1002/cphc.200600309... 

For several reasons, PMR studies on dinucleotides are difficult. In the case of a homodinucleotide, the difference between the chemical shifts of the protons of the 3 -bound nucleoside and the 5 -bound one are rather small, particularly for the sugar protons, and thus difficult to identify. Analysis of the protons of the bases is easier, since one expects changes in chemical shifts of stacked bases (see also Section 6.3.1) due to the ring current. Still, many studies (46) have appeared in which it was concluded that all dinucleotides were in a right-handed ant/-an /-conformation. This conclusion appears to be justified for the homooligonucleotides, but possibly may not extend beyond that. To avoid overlap of the peaks of the two nucleosides, one of them might be completely deuterated. This has been done (47), and the study on ApA confirmed the previous optical data. The synthesis of such a deuterated dinucleotide is, however, not a simple affair. 

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