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