Parameter and structural identifiability concepts and ambiguities: a critical review and analysis

The notion of identifiability addresses the question of whether it is at all possible to obtain unique solutions for unknown parameters of interest in a mathematical model, from data collected in well-defined stimulus-response experiments performed on a dynamic system represented by the model. This critical aspect of the modeling and data reduction problem is reviewed, analyzed, and unified, with emphasis on applications in biology. Several physiological system models are examined in detail. They illustrate the importance of identifiability analysis prior to performing a parameter estimation experiment, the algebraic difficulties, possible pitfalls, and not-so-apparent ambiguities that may be encountered--even for simple models--and the utility of the concept in experiment design. Methods for testing for identifiability also are reviewed and compared, with emphasis on applicability and limitations. The usefulness of a given model for predicting the time course of system variables (not parameters) of interest normally inaccessible to direct measurement (e.g., tissue concentrations), a common use for quantitative models, is shown to depend intimately on the identifiability properties of the model, in a manner not easy but essential to assess: state variable predictions made in this manner can be inherently ambiguous.