The Subject-by-Formulation Interaction as a Criterion of Interchangeability of Drugs

Abstract

SUMMARY The primary purpose of a bioequivalence study is often to meet the regulatory requirement of similar average bioavailabilities. This is usually done by estimating the mean difference between formulations in a crossover design. However, a small difference, as well as a rather narrow confidence interval, might be obtained also if the subjects respond differently to the formulations, i.e., if there is a nonnegligible subject-by-formulation interaction. Hence, it can be argued that this interaction should be part of the criterion of interchangeability. To be able to study this interaction the ordinary simple crossover design is not appropriate. Instead, a design where each formulation is administered at least twice to each subject is desirable. Such a design is obtained by repeating a simple crossover layout. To evaluate the impact of the subject-by-formulation interaction, the ratio of the variance components of the interaction and the error is estimated. This approach is illustrated by an example. Two different formulations of a drug are considered bioequivalent if their average bioavailabilities are similar. The assessment of this similarity is usually based on an interval estimate of the mean difference between the formulations. However, this focus on means is an insufficient criterion, since a small difference, as well as a rather narrow confidence interval, might be obtained also if the formulation differences show a considerable variation among subjects. The impact on drug interchangeability of this so-called subject-byformulation interaction is discussed, for example, by Hwang et al. (1978). In order to estimate this interaction they suggest a design where each formulation is administered at least twice to each subject. In this paper we briefly discuss how to design and analyze a bioequivalence study in order to evaluate the impact of the subject-by-formulation interaction. As a measure of the magnitude of the interaction we propose the ratio of the variance components of the interaction and the error. The ideas of the paper are illustrated with data from a comparative study of two generic formulations of furosemide.