Modelling Response Time Profiles in the Absence of Drug Concentrations: Definition and Performance Evaluation of the K–PD Model

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Abstract
The plasma concentration–time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK50 which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC50, the pharmacodynamic potency, and clearance, the PK “potency” at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC50 to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK–PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K–PD model should definitively not be substituted for the gold standard PK–PD model when correct full model can and should be identified.