Analysis of a 3-period 2-treatment pharmacokinetic study to assess scaled average bioequivalence

In the past years various approaches for assessing bioequivalence of so-called "highly variable drugs" have been debated. These are drugs whose pharmacokinetic profiles vary considerably when given to the same subject. As a consequence of the high variability, average bioequivalence between two such drugs can only be shown with an unfeasibly high number of subjects. Therefore regulatory agencies generally agree that the criterion of average bioequivalence warrants adjustment for highly variable drugs. The mainstream of the most recent discussion favours an approach that is called scaled average bioequivalence. With this approach the usual criterion of average bioequivalence is scaled by the within-subject standard deviation of the pharmacokinetic parameter in question. A parsimonious design for evaluating scaled average bioequivalence is a three-period two-treatment crossover trial where the reference drug is given twice and the investigational drug is given once to each subject. In this paper it is shown how to analyse the data of such a trial with respect to the criterion of scaled average bioequivalence under the assumption of a log-normal distribution of the pharmacokinetic parameter. Explicit SAS code for the analysis is provided. INTRODUCTION "Highly variable drugs" are called drugs whose pharmacokinetic profiles vary considerably when given to the same subject. For highly variable drugs the FDA presented possible alternatives to the average bioequivalence method in a meeting of the Advisory Committee for Pharmaceutical Science (ACPS) in April 2004. The committee favoured a scaled approach where the bioequivalence limits are expanded based on the within-subject variability of the reference product (cf. [1]). Specifically, let Y denote the log-transformed values (natural logarithm: ln) of the area under the plasma concentration time curve (AUC) or the maximum concentration (Cmax). Let μR and μT denote the mean values of Y for the reference and the test product, respectively, and let σR denote the within-subject standard deviation of Y for the reference product. The criterion for scaled average bioequivalence requires the following null hypothesis to be rejected at a significance level of 5%: (1) H0: | μT − μR | > θA ( σR / σ0 ) where θA is ln(1.25), the limit for average bioequivalence, and σ0 is a scaling constant. The scaling constant σ0 needs to be agreed upon. Values between 0.2 and 0.3 are under discussion. A scaling constant of 0.25 would imply that the average bioequivalence criterion θA is expanded for drugs with a coefficient of variation of about 25% or higher. In fact, the current definition of highly variable drugs is a within-subject coefficient of variation of 30% or more for the AUC or Cmax [2]. For the log-transformed variable Y this corresponds to a within-subject standard deviation of 0.2936 or higher provided Y is normally distributed. Generally, for a log-normally distributed variable X the coefficient of variation γ of X and the standard deviation σ of ln(X) are related by