Bias of two one-sided tests procedures in assessment of bioequivalence.

The current applications of Schuirmann's two one-sided tests procedure for the original scale ignore the variability of the least squares mean of the reference formulation when it substitutes for the unknown reference average of pharmacokinetic responses. We propose a modified two one-sided test procedure that takes into account the variability of the least squares mean of the reference formulation. The non-parametric version of the modified procedure is also available. We conducted a simulation study to examine the true level of significance and empirical power of four current parametric and non-parametric two one-sided tests procedures under a 2 x 2 crossover design with different combinations of sample size, intrasubject variability, and correlation between the two responses from a subject. Both theoretical results and empirical evidence show that the true level of significance of the current two one-sided tests procedures converges to 0.5 when the correlation of the two responses approaches 1. However, not only is the modified two one-sided tests procedure a test of size alpha, but empirical evidence indicates it is also an unbiased test. The modified non-parametric procedure also controls the size of the tests and is competitive even under normality assumption.