Robustness of bioequivalence procedures under Box-Cox alternatives

The robustness of Schuirmann's two one-sided tests procedure is investigated under a set of Box-Cox alternatives. Schuirmann's procedure is currently employed to assess the bioequivalence on the average bioavailability between two drug formulations with normality or lognormality assumptions of the observed pharmacokinetic data, which are often not met in practice. Distribution of the phamacokinetic data is discussed and the exact moments of the distribution are derived in a close form for a special case. The level of significance and the power of the procedure are studied through simulations, where numerical integration is applied and statistical software SAS and S-PLUS are used. The simulation results are fitted into linear additive models for analytic purposes. The study shows that Schuirmann's two one-sided tests procedure is robust under the Box-Cox alternatives when the mean of the underlying distribution of the reference formulation is known, which suggests that the normality or lognormality assumptions are sufficient but may not be necessary in this case. It appears that Schuirmann's procedure cannot maintain the proper level of significance when the mean of the underlying distribution of the reference formulation is unknown, even under the normality or lognormality assumptions. It is also found that the coefficient of variation, the sample size, the correlation coefficient of the two responses from each subject, and knowledge of the distribution of the reference formulation affect the behavior of Schuirmann's procedure.