Statistical Identification of Multivariate Outliers with Applications to Bioequivalence Evaluation

The most commonly employed design for bioequivalence studies is the two-sequence and two-period ( ) crossover design under which a linear mixed-effects model is applied to make statistical inference of evaluation of average bioequivalence (ABE). Outlying subjects are unusual subjects with extremely high or low bioavailability of the test formulation relative to the reference formulation; or with extreme bioavailabilities to both formulations as compared to other subjects. Inclusion or exclusion of outlying subjects may lead to a completely difference conclusion of ABE. Likelihood distance (LD), Estimates distance (ED) and Hotelling T2 (HT) have been proposed for detection of outlying subject. However, these methods are not based on the maximum of the central chi-square random variables or they are based on empirical critical values obtained from the simulations. To overcome these drawbacks, based on the Fisher-Tippett theorem, we derived the asymptotic distribution of the maximum of Hotelling T2 statistic for the inference of detection of an outlying subjects. Simulation studies were conducted to investigate and compare the performance, in terms of size and power, of our proposed procedure. Real data illustrate the application of our proposed method.