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In this dissertation, a multivariate generalization of the criterion used for testing individual bioequivalence is proposed. Although various approaches have been reported in the literature for multivariate equivalence, the majority of these contemplate simultaneous comparisons of only means in each dimension for multivariate equivalence region. Unlike previous approaches, our proposed criterion combines not only the comparison of means and variances but also the within-subject correlations into a single aggregate criterion. In fact, in this research two multivariate criteria for testing of individual bioequivalence have been developed. The first criterion is based on traces of variance-covariance matrices of test and reference formulation hence ignores the correlation among pharmacokinetic parameters. Hence, for this criterion, the consideration of extension from univariate to multivariate could be questionable. Therefore, another criterion has been developed which is unlike the previous one and it involves the correlation among pharmacokinetic parameters. Finally, thesecond criterion is proposed as a multivariate generalization for testing of individual bioequivalence which is an actual multivariate extension of univariate individual bioequivalence approved by Food and Drug Administration. The proposed method is also illustrated by testing individual bioequivalence on Food and Drug Administration dataset. The exact distribution of proposed criterion is hard to drive, therefore, the bootstrap method as recommended by Food and Drug Administration is proposed. The performance of proposed multivariate individual bioequivalence criterion has been evaluated through a simulation study. The size and power of testing for individual bioequivalence using proposed multivariate criterion are determined by varying mean differences, within-subject variances, sample sizes as well as within-subject correlations between pharmacokinetic parameters.
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