Simultaneous modeling of pharmacokinetics and pharmacodynamics with nonparametric kinetic and dynamic models

Abstract

Three models, linked in series, can be used to analyze combined pharmacokinetic (PK) and pharmacodynamic (PD) data arising from non--steady-state experiments. A PK model relates dose to plasma drug concentration (Cp); a link model relates Cp to drug concentration at the effect site (Ce); and a PD model relates Ce to drug effect (E). All three submodels can be stated parametrically. Recently the use of a nonparametric PD submodel has been proposed (CLIN PHARMACOL THER 1984;35:733-41). In this article we use an extended nonparametric approach that represents both the PK and PD models nonparametrically, but retains a parametric link model. Cp data from several PK models and E data from several PD models were simulated. After the addition of noise to both the Cp and E data, they were analyzed by both the parametric and extended nonparametric methods. The methods were compared by how well they estimated the PD model. To assess robustness, the effect of misspecification of the PK submodel on the goodness of estimation of both methods was also compared. In the absence of model misspecification, the parametric method usually estimates the PD model better than the nonparametric method. However, this difference in the performances diminishes and even reverses when the PK model is misspecified. Because one can rarely be certain that model misspecification is absent, the nonparametric approach may offer a distinct advantage for routine analysis of PK/PD data.

Pharmacokinetic–pharmacodynamic model for perindoprilat regional haemodynamic effects in healthy volunteers and in congestive heart failure patients

“…Perindoprilat concentration (ng ml E max =x41%, CE 50 =4.95 ng ml x1 , c =2. 25, and E 0 =0 in HV, and E max =x60%, CE 50 =1.38 ng ml x1 , c =3.06, and E 0 =0 in CHF patients.…”

A ‘bottom‐up’ approach for endo‐PK/PD analysis

“…Several models have been investigated and proposed to establish the nature of the PD relationship [21,22]. A number of different methodologies have also been developed from the traditional structured modeling approaches [23,24] to the nonparametric developments using hysteresis minimization principles [3,[25][26][27].…”

Simultaneous versus sequential pharmacokinetic‐pharmacodynamic population analysis using an Iterative Two‐Stage Bayesian technique

“…From a statistical point of view this approach is not ideal, because the PK parameters are treated as errorfree constants in the PD analysis, while in fact they are known with a limited precision only. An alternative approach using the PK data directly without a separate PK analysis was described by Unadkat and colleagues [3]. This 'nonparametric PK method' suffers from the same statistical flaws as the sequential method.…”