AJP - Regulatory, Integrative and Comparative Physiology, Vol 239, Issue 1 7-24, Copyright © 1980 by American Physiological Society
Parameter and structural identifiability concepts and ambiguities: a critical review and analysis
C. Cobelli and J. J. DiStefano 3rd
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.
