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* for a replicate design account for VarD; * for example here, set VarD=0; varD=0.0; s = sqrt(varD + sigmaW*sigmaW); It is worth noting here that REML modelling in replicate designs and the resulting ABE assessments are sensitive to the way in which the variance-covariance matrix is constructed (Patterson and Jones, 2002a). The recommended FDA procedure (FDA Guidance, 2001) provides bi-ased variance estimates (Patterson and Jones, 2002c) in certain situa-tions; however, it also constrains the Type I error rate to be less than 5% for average bioequivalence due to the constraints placed on the variance-covariance parameter space, which is a desirable property for regulators reviewing such data. 7.7 Kullback–Leibler divergence Dragalin and Fedorov (1999) and Dragalin et al. (2002) pointed out some disadvantages of using the metrics for ABE, PBE and IBE, that we have described in the previous sections, and proposed a unified approach to equivalence testing based on the Kullback–Leibler divergence (KLD) (Kullback and Leibler, 1951). In this approach bioequivalence testing is regarded as evaluating the distance between two distributions of selected pharmacokinetic statistics or parameters for T and R. For example, the selected statistics might be log(AUC) or log(Cmax), as used in the previous sections. To demonstrate bioequivalence, the following hypotheses are tested: H : d(f ) > d vs. H , (7.15) where f are the appropriate density functions of the observa-tions from T and R, respectively, and d is a pre-defined boundary or goal-post. Equivalence is determined if the following null hypothesis is rejected. For convenience the upper bound of a 90% confidence interval, d . If d then bioequivalence is accepted; otherwise it is rejected. Under the assumption that T and R have the same variance, i.e., σ , the KLD for ABE becomes (µ −µ ) d( fT , f σ2 which differs from the (unscaled) measure defined in Section 4.2. If the statistics (e.g., log(AUC)) for T and R are normally distributed with means µ , respectively, and variances σ
DOI link for * for a replicate design account for VarD; * for example here, set VarD=0; varD=0.0; s = sqrt(varD + sigmaW*sigmaW); It is worth noting here that REML modelling in replicate designs and the resulting ABE assessments are sensitive to the way in which the variance-covariance matrix is constructed (Patterson and Jones, 2002a). The recommended FDA procedure (FDA Guidance, 2001) provides bi-ased variance estimates (Patterson and Jones, 2002c) in certain situa-tions; however, it also constrains the Type I error rate to be less than 5% for average bioequivalence due to the constraints placed on the variance-covariance parameter space, which is a desirable property for regulators reviewing such data. 7.7 Kullback–Leibler divergence Dragalin and Fedorov (1999) and Dragalin et al. (2002) pointed out some disadvantages of using the metrics for ABE, PBE and IBE, that we have described in the previous sections, and proposed a unified approach to equivalence testing based on the Kullback–Leibler divergence (KLD) (Kullback and Leibler, 1951). In this approach bioequivalence testing is regarded as evaluating the distance between two distributions of selected pharmacokinetic statistics or parameters for T and R. For example, the selected statistics might be log(AUC) or log(Cmax), as used in the previous sections. To demonstrate bioequivalence, the following hypotheses are tested: H : d(f ) > d vs. H , (7.15) where f are the appropriate density functions of the observa-tions from T and R, respectively, and d is a pre-defined boundary or goal-post. Equivalence is determined if the following null hypothesis is rejected. For convenience the upper bound of a 90% confidence interval, d . If d then bioequivalence is accepted; otherwise it is rejected. Under the assumption that T and R have the same variance, i.e., σ , the KLD for ABE becomes (µ −µ ) d( fT , f σ2 which differs from the (unscaled) measure defined in Section 4.2. If the statistics (e.g., log(AUC)) for T and R are normally distributed with means µ , respectively, and variances σ
* for a replicate design account for VarD; * for example here, set VarD=0; varD=0.0; s = sqrt(varD + sigmaW*sigmaW); It is worth noting here that REML modelling in replicate designs and the resulting ABE assessments are sensitive to the way in which the variance-covariance matrix is constructed (Patterson and Jones, 2002a). The recommended FDA procedure (FDA Guidance, 2001) provides bi-ased variance estimates (Patterson and Jones, 2002c) in certain situa-tions; however, it also constrains the Type I error rate to be less than 5% for average bioequivalence due to the constraints placed on the variance-covariance parameter space, which is a desirable property for regulators reviewing such data. 7.7 Kullback–Leibler divergence Dragalin and Fedorov (1999) and Dragalin et al. (2002) pointed out some disadvantages of using the metrics for ABE, PBE and IBE, that we have described in the previous sections, and proposed a unified approach to equivalence testing based on the Kullback–Leibler divergence (KLD) (Kullback and Leibler, 1951). In this approach bioequivalence testing is regarded as evaluating the distance between two distributions of selected pharmacokinetic statistics or parameters for T and R. For example, the selected statistics might be log(AUC) or log(Cmax), as used in the previous sections. To demonstrate bioequivalence, the following hypotheses are tested: H : d(f ) > d vs. H , (7.15) where f are the appropriate density functions of the observa-tions from T and R, respectively, and d is a pre-defined boundary or goal-post. Equivalence is determined if the following null hypothesis is rejected. For convenience the upper bound of a 90% confidence interval, d . If d then bioequivalence is accepted; otherwise it is rejected. Under the assumption that T and R have the same variance, i.e., σ , the KLD for ABE becomes (µ −µ ) d( fT , f σ2 which differs from the (unscaled) measure defined in Section 4.2. If the statistics (e.g., log(AUC)) for T and R are normally distributed with means µ , respectively, and variances σ
ABSTRACT