Target-mediated drug disposition model: approximations, identifiability of model parameters and applications to the population pharmacokinetic–pharmacodynamic modeling of biologics

Models for drugs exhibiting target-mediated drug disposition (TMDD) describe biological processes in which drug-target binding significantly influences both pharmacodynamics (PD) and pharmacokinetics (PK). TMDD models are often over-parameterized and their parameters are difficult to estimate based on available data. Approximations of the general model have been suggested, but even these simpler forms can be over-parameterized when, for example, target and drug-target complex concentrations are not available. This work i) reviews TMDD equations, their approximations and methods to study identifiability of model parameters; ii) reviews the publications that used TMDD equations to describe PK and PD of biologics; and iii) discusses issues of identifiability of the TMDD model parameters related to study design and data analysis. Examples demonstrate that use of the TMDD equations for the population PK and PD modeling is most successful when the target and drug-target complex concentrations are available in addition to the drug concentration data. TMDD parameter estimates can be trusted only when they are identifiable, that is, can be estimated from the available data with sufficient precision. Parameter identifiability analysis should be an integral part of the TMDD system investigation. It also should be used prospectively for optimal study design.