Simultaneous modeling of pharmacokinetics and pharmacodynamics with a nonparametric pharmacodynamic model

We describe a variation on an approach to simultaneous modeling of pharmacokinetics (PK) and pharmacodynamics (PD). Both approaches model the often-observed time lag between plasma drug concentration (Cp) and drug effect (E) in non-steady-state experiments by postulating an E site whose concentration (Ce) is kinetically linked to Cp by a first-order process. With the linking model, the time lag can be removed from the data and the underlying concentration-response (Ce-E) relationship can be estimated. The original method requires the analyst to postulate a particular parametric form for the Ce-E model, whereas ours does not. It estimates the rate constant of the linking model as the value that causes the hysteresis curve (Ce vs E points connected in time order) to collapse to a single curve that represents the (empirical) Ce-E relationship. The method is presented as an algorithm and is tested by means of simulation and a real-world example. The results suggest that the method can faithfully estimate the Ce-E curve for a variety of PD models and degrees of experimental error when its basic assumption of time-invariant PD holds.