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and σ +σ { , respectively, the KL } D ( for PBE ) is 111d(f ) = (µ −µ ) + − 2. (7.17) 2 σ For IBE, the { KLD is 1 }( ) d(f ) = (µ +σ + 2 − 2, 2 σ σWR (7.18) where σ = Var(s ) = σ − 2ρσ σBR . Advantages of using the KLD are that it: (1) possesses a natural hi-erarchical property such that IBE implies PBE and PBE implies ABE, (2) satisfies the properties of a true distance metric, (3) is invariant to monotonic transformations of the data, (4) generalizes easily to the mul-tivariate case where equivalence on more than one parameter (e.g., AUC, Cmax and Tmax) is required and (5) is applicable over a wide range of distributions of the response variable (e.g., those in the exponential fam-ily). Patterson et al. (2001) and Dragalin et al. (2002), described the results of a simulation study and a retrospective analysis of 22 replicate design datasets, to compare testing for IBE using the KLD with testing based on the FDA-recommended metric defined earlier in Section 7.4. One notable finding of these studies was that the KLD metric identified more datasets as being of concern than the FDA-recommended metric. This appeared to be due to ability of the FDA-recommended metric to reward novel formulations for which the within-subject variance is decreased relative to the reference. 7.8 Modelling pharmacokinetic data Although AUC and Cmax are adequate for testing for bioequivalence, there is sometimes a need to model the drug concentrations over time. Fitting such models aids the understanding of how the drug is absorbed and eliminated from the body, as well as allowing model-based estimates of AUC and Cmax to be obtained. A popular type of model that is fitted in these circumstances is the compartmental model, which considers the body as made up of a number of compartments through which the drug circulates. For example, the circulating blood might be considered as the single compartment in a one-compartment model. If a drug is taken orally as a tablet, say, the drug is absorbed into this compartment as the tablet dissolves in the stomach and is eliminated from this compartment by (among other things) the actions of the liver and kidneys. While the tablet is still being dissolved in the stomach, the rate of absorption of the drug into the circulating blood is greater than the rate that is eliminated
DOI link for and σ +σ { , respectively, the KL } D ( for PBE ) is 111d(f ) = (µ −µ ) + − 2. (7.17) 2 σ For IBE, the { KLD is 1 }( ) d(f ) = (µ +σ + 2 − 2, 2 σ σWR (7.18) where σ = Var(s ) = σ − 2ρσ σBR . Advantages of using the KLD are that it: (1) possesses a natural hi-erarchical property such that IBE implies PBE and PBE implies ABE, (2) satisfies the properties of a true distance metric, (3) is invariant to monotonic transformations of the data, (4) generalizes easily to the mul-tivariate case where equivalence on more than one parameter (e.g., AUC, Cmax and Tmax) is required and (5) is applicable over a wide range of distributions of the response variable (e.g., those in the exponential fam-ily). Patterson et al. (2001) and Dragalin et al. (2002), described the results of a simulation study and a retrospective analysis of 22 replicate design datasets, to compare testing for IBE using the KLD with testing based on the FDA-recommended metric defined earlier in Section 7.4. One notable finding of these studies was that the KLD metric identified more datasets as being of concern than the FDA-recommended metric. This appeared to be due to ability of the FDA-recommended metric to reward novel formulations for which the within-subject variance is decreased relative to the reference. 7.8 Modelling pharmacokinetic data Although AUC and Cmax are adequate for testing for bioequivalence, there is sometimes a need to model the drug concentrations over time. Fitting such models aids the understanding of how the drug is absorbed and eliminated from the body, as well as allowing model-based estimates of AUC and Cmax to be obtained. A popular type of model that is fitted in these circumstances is the compartmental model, which considers the body as made up of a number of compartments through which the drug circulates. For example, the circulating blood might be considered as the single compartment in a one-compartment model. If a drug is taken orally as a tablet, say, the drug is absorbed into this compartment as the tablet dissolves in the stomach and is eliminated from this compartment by (among other things) the actions of the liver and kidneys. While the tablet is still being dissolved in the stomach, the rate of absorption of the drug into the circulating blood is greater than the rate that is eliminated
and σ +σ { , respectively, the KL } D ( for PBE ) is 111d(f ) = (µ −µ ) + − 2. (7.17) 2 σ For IBE, the { KLD is 1 }( ) d(f ) = (µ +σ + 2 − 2, 2 σ σWR (7.18) where σ = Var(s ) = σ − 2ρσ σBR . Advantages of using the KLD are that it: (1) possesses a natural hi-erarchical property such that IBE implies PBE and PBE implies ABE, (2) satisfies the properties of a true distance metric, (3) is invariant to monotonic transformations of the data, (4) generalizes easily to the mul-tivariate case where equivalence on more than one parameter (e.g., AUC, Cmax and Tmax) is required and (5) is applicable over a wide range of distributions of the response variable (e.g., those in the exponential fam-ily). Patterson et al. (2001) and Dragalin et al. (2002), described the results of a simulation study and a retrospective analysis of 22 replicate design datasets, to compare testing for IBE using the KLD with testing based on the FDA-recommended metric defined earlier in Section 7.4. One notable finding of these studies was that the KLD metric identified more datasets as being of concern than the FDA-recommended metric. This appeared to be due to ability of the FDA-recommended metric to reward novel formulations for which the within-subject variance is decreased relative to the reference. 7.8 Modelling pharmacokinetic data Although AUC and Cmax are adequate for testing for bioequivalence, there is sometimes a need to model the drug concentrations over time. Fitting such models aids the understanding of how the drug is absorbed and eliminated from the body, as well as allowing model-based estimates of AUC and Cmax to be obtained. A popular type of model that is fitted in these circumstances is the compartmental model, which considers the body as made up of a number of compartments through which the drug circulates. For example, the circulating blood might be considered as the single compartment in a one-compartment model. If a drug is taken orally as a tablet, say, the drug is absorbed into this compartment as the tablet dissolves in the stomach and is eliminated from this compartment by (among other things) the actions of the liver and kidneys. While the tablet is still being dissolved in the stomach, the rate of absorption of the drug into the circulating blood is greater than the rate that is eliminated
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