New models for pharmacokinetic data based on a generalized Weibull distribution

We consider the development of the concentration of a drug in the blood after single oral or intravenous administration. We introduce a new nonlinear model capable of describing concentration-time curves following intravenous administration. A similar model is proposed for oral data. Both models have four parameters, of which two regulate the shape of the curve and two determine the scale of the time and concentration axes. All the parameters are closely related to geometric properties of the curve. The scale parameters determine a point in the curve, and the shape parameters can be calculated by using numerical integration. The models can be used when the object of the analysis is to quantify the shape of a concentration-time curve. We discuss the usefulness of the models in bioequivalency trials, in clinical safety and efficacy trials, and in population pharmacokinetics. The models are applied to two previously presented data sets. To reduce the number of parameters, the shape parameters are assumed common for all individuals. Encouraging results are obtained. We also present a new four-parameter Michaelis-Menten model.