Determining identifiable parameter combinations using subset profiling

• A new computational approach to identifiable combinations is presented.
• This method combines the Fisher Information Matrix and profile likelihood.
• A parameter subset selection condition is used to condition the profile likelihood.
• The subset profiling method recovers the form of the identifiable combinations.
• The method is demonstrated on examples from cell biology and physiology.

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the dependencies between unidentifiable parameters. Identifiable combinations can help in model reparameterization and also in determining which parameters may be experimentally measured to recover model identifiability. Several numerical approaches to determining identifiability of differential equation models have been developed, however the question of determining identifiable combinations remains incompletely addressed. In this paper, we present a new approach which uses parameter subset selection methods based on the Fisher Information Matrix, together with the profile likelihood, to effectively estimate identifiable combinations. We demonstrate this approach on several example models in pharmacokinetics, cellular biology, and physiology.