Kinetic-pharmacodynamic model for drugs with non-linear elimination: parameterisation matters.

Kinetic-pharmacodynamic (KPD) models are used to predict the time course and magnitude of drug effects in the absence of pharmacokinetic (PK) data. They have found utility in situations where it is not possible or feasible to collect plasma concentration data, but where a pharmacodynamic (PD) marker can be measured. In this case, a KPD model can be fitted to the PD data while the ‘kinetic’ behaviour of the drug is inferred. In most cases, the ‘kinetic portion of the KPD model is represented by a standard one-compartment model with intravenous bolus input and linear elimination. Two parameterisations have been proposed for linking the ‘kinetic’ and PD portions in a KPD model. Most commonly, the elimination rate of the drug from the ‘kinetic’ compartment is estimated and used to drive the PD effect. For an inhibitory function this is given by;