On testing structural identifiability by a simple scaling method: Relying on scaling symmetries can be misleading

Abstract

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.

Symmetries in Dynamic Models of Biological Systems: Mathematical Foundations and Implications

“…While they are arguably the most commonly found type of symmetry, dynamic models of biological systems may admit symmetry transformations of other types, instead or in addition to scaling. Since the absence of scaling symmetries does not exclude the existence of other types, caution must be exercised when interpreting the results of analyses based exclusively on scalings [25].…”

“…It detects scaling symmetries, which are arguably the most frequently found in biological models. However, it must be taken into account that, if a model contains other types of symmetries, the results of SIM do not inform about structural identifiability [25].…”

AutoRepar: A method to obtain identifiable and observable reparameterizations of dynamic models with mechanistic insights

“…More specifically, model reduction based on nondimensionalization amounts to a rescaling of model variables. Scaling symmetries are one of the types of symmetries encountered in dynamical models; 53 a further explanation of the relation between scaling symmetries and nondimensionalization can be found in Reference 54.…”