A two one-sided tests procedure for assessment of individual bioequivalence

In this paper we propose a two one-sided tests procedure for assessment of individual bioequivalence based on the concept of individual equivalence ratios proposed by Anderson and Hauck. The proposed procedure is derived under the normality assumption for the logarithmic transformation of pharmacokinetic responses obtained from a standard two-sequence, two-period crossover design. We show that the hypotheses for individual bioequivalence are equivalent to the hypotheses for testing whether the upper (or lower) pth quantile of the distribution of the differences between the test and reference formulations from the same subject is not greater (or not smaller) than some prespecified equivalence limits. Under this setting, we examine the relationship between average and individual bioequivalence. There exists the uniformly most powerful invariant test for each of the two one-sided hypotheses. In addition, the proposed two one-sided tests procedure is a test of size alpha (i.e., < or = alpha). We demonstrate that the determination of critical values, the enumeration of power, and the estimation of sample sizes requires noncentral t-distributions but does not necessarily require the estimation of unknown population mean and variance for noncentrality parameters. We discuss possible extensions to other crossover and replicated crossover designs. A numerical example illustrates the proposed procedure.