Deterministic identifiability of population pharmacokinetic and pharmacokinetic–pharmacodynamic models

Identifiability is an important component of pharmacokinetic–pharmacodynamic (PKPD) model development. Structural identifiability is concerned with the uniqueness of the model parameters for a set of perfect input–output data and deterministic identifiability with the precision of parameter estimation given imperfect input–output data. We introduce two subcategories of deterministic identifiability, external and internal, and consider factors that distinguish between these forms. We define external deterministic identifiability as a function of externally controllable variables, i.e., the design, and internal deterministic identifiability as a function of the model and its parameter values. The concepts are explored using three common PK and PKPD models, and verified for their precision for the selected set of parameter values under optimal design.