Use of a pharmacokinetic/pharmacodynamic model to design an optimal dose input profile

A model for the pharmacodynamic effect of a drug (designated only X), and the use of the model to explore optimal input is described. The data analyzed here are from a crossover comparison study of the effect of 4 active treatments, yielding distinct concentration vs. time curves, plus placebo in 32 subjects. The model expresses total effect as the sum of placebo effect and (pure) drug effect. The latter allows for possible tolerance (found) and time effects (not found). Random effects allow interindividual differences to be expressed. Conditioning on the fitted model, a population optimal input profile is designed that obeys certain protocol constraints. The profile minimizes the expectation of a sum of squared differences between target effect and the resulting response over a given time interval. The target is a fixed constant, chosen to be either the individuals' maximum effect level in response to a baseline input regimen used in the study or the maximum effect level for the typical individual in the population in response to this regimen, as predicted from the model. The expectation is taken over the estimated nonparametric distribution of the 32 subjects' random effects. As one goal of early clinical studies of drugs may be to provide a basis for designing an optimal delivery profile (with respect to a specified loss function), we suggest this report as an example of a reasonable way to go about finding such a profile.