Semiparametric approach to pharmacokinetic-pharmacodynamic data

A semiparametric model for analysis of pharmacokinetic (PK) and pharmacodynamic (PD) data arising from non-steady-state experiments is presented. The model describes time lag between drug concentration in a sampling compartment, e.g., venous blood (Cv), and drug effect (E). If drug concentration at the effect site (Ce) equilibrates with arterial blood concentration (Ca) slower than with Cv, a non-steady-state experiment yields E vs. Cv data describing a counterclockwise hysteresis loop. If Ce equilibrates with Ca faster than with Cv, clockwise hysteresis is observed. To model hysteresis, a parametric model is proposed linking (unobserved) Ca to Cv with elimination rate constant kappa ov and also linking Ca to Ce with elimination rate constant kappa oe. When kappa oe is greater than (or less than) kappa ov clockwise (or counterclockwise) hysteresis occurs. Given kappa oe and kappa ov, numerical (constrained) deconvolution is used to obtain the disposition function of the arterial compartment (Ha), and convolution is used to calculate Ce given Ha. The values of kappa oe and kappa ov are chosen to collapse the hysteresis loops to single curves representing the Ce-E (steady-state) concentration-response curve. Simulations, and an application to real data, are reported.