A multivariate test for population bioequivalence

In this article, we propose a multivariate generalization of the criteria for testing univariate population bioequivalence. Recently, a number of approaches for testing multivariate equivalence have appeared in the literature. Most of them consider a multivariate equivalence region, which implies simultaneous comparison of means in each dimension. In contrast, our proposal combines a comparison of means and a comparison of variances into a single aggregate criterion, using the trace of the covariance matrix as a scalar measure of the total variability. We use a confidence interval approach to multivariate population bioequivalence testing, similar to the univariate case. Two versions of the modified large-sample confidence interval for the linearized multivariate criterion are constructed. In a simulation study, we evaluate the empirical coverage of these confidence intervals and rejection rates of the corresponding tests in finite samples. The proposed methodology is illustrated with an example of testing equivalence of the spray pattern of nasal sprays.