Use of a Generalized Multivariate Gamma Distribution Based on Copula Functions in the Average Bioequivalence

Abstract

Bioequivalence studies have been generally used to compare a test formulation with a reference, in order to validate the interchangeability between them. Some pharmacokinetic (PK) parameters are compared in this type of study, typically using a model which assumes independence among PK parameters, the same variance for the different formulations, logarithmic transformation for the data and normal distribution for the residuals. We propose an alternative model based on a generalized gamma distribution, which permits the presence of positive asymmetry for the data and possible differences in the variances for the different formulations which could have more flexibility in this case. For the multivariate structure, we use a Gaussian copula function to capture the possible dependence between the PK parameters. We use Bayesian inference methods to obtain the results of interest. We also introduce a real data example from where we observe a good fit of the proposed model for the dataset. From this study, we conclude that the proposed model could be a good alternative in some applications where the distribution of the bioequivalence data presents a positive asymmetric distribution.