A practical approach for evaluating population and individual bioequivalence.

Pharmacokinetic measurements provided by subjects to each of two formulations of a drug have a joint distribution that can be characterized by parameters reflecting scale and correlation as well as location. The bioavailability of the formulations can be expressed in terms of the means of the marginal distributions, their means and variances, or the marginal means and variances and the joint correlation. These expressions correspond, respectively, to 'average', 'population', and 'individual' bioequivalence when the joint distribution of the measurements is bivariate normal. Current proposals for assessing the degree of bioequivalence of two formulations are based on statistics that are composites of variance components and squares of expected mean differences from a mixed linear model. There are technical and practical issues associated with these proposals, particularly that they require more complicated designs than the familiar 2x2 cross-over. This paper describes an alternative approach that can be applied with standard 2x2 cross-over designs, and that provides evaluations of population and individual bioequivalence that should be adequate for all practical clinical purposes. The approach is based on easily computed correlation and regression coefficients whose statistical properties under normality are well known and for which non-parametric and robust alternatives exist when normality cannot be assumed. The approach yields conclusions consistent with those obtained by the current proposals when applied to data sets supplied by the FDA. In the cases where the conclusions do not match, the new approach appears to be more consistent with the data.