Bayesian knowledge integration for an in vitro–in vivo correlation (IVIVC) model
Elvira M. Erhardt (1), Moreno Ursino (2), Tom Jacobs (3), Jeike Biewenga (3), Mauro Gasparini (1)
(1) Politecnico di Torino, Turin, Italy, (2) INSERM, University Paris 5 and 6, France (3) Janssen Pharmaceutica NV, Beerse, Belgium
In vitro–in vivo correlation (IVIVC) methods play a key role in the drug development and optimization of formulations. An IVIVC is defined by the Food and Drug Administration as the mathematical relationship between the in vitro characteristics of a dosage form and its in vivo response. This tool can act as a surrogate for bioequivalence or bioavailability testing in human subjects, thus support biowaivers and thereby reduce cost and duration of the optimization process . However, most of the current IVIVC models entail complex and potentially unstable mathematical deconvolution operations and are assessed applying purely frequentist methods, such as linear regression, on averaged data . We suggest a new predictive model for the pharmacokinetic (PK) data of a controlled release (CR) formulation through combination of an in vitro model of the drug release with an in vivo immediate release (IR) model. Simultaneously, we account for the uncertainty in the parameter estimates.
The proposed 3-step IVIVC approach includes (a) a frequentist nonlinear mixed effects model  for the in vitro release data; (b) a frequentist population PK compartment model for the in vivo IR data (fitted using the NLMIXR package  in R); and (c) a system of ordinal differential equations containing the submodels (a) and (b), which approximates and predicts the in vivo blood concentration-time, using in vivo controlled release data. The innovation consists of splitting the parameter space between submodels (a) and (b) versus (c) and, subsequently, accounting for the uncertainty around these parameters via a Bayesian framework (in the software STAN ). That is, estimates from the first two frequentist submodels serve as priors for the Bayesian hierarchical third submodel; the prior standard deviations account for the variability around the previously estimated parameters . We demonstrate the application of the method using the study data of a transdermal patch, in (a) and (c), and of an intravenous infusion, in (b), as an example.
The in vitro release was well-approximated by a Weibull input-function; a three-compartment model described the IR concentration data of the population PK adequately. The combined ODE converged with a reasonable run-time and the predicted drug concentration-time profiles are comparable with the in vivo observations. Thus, the developed IVIVC model led to a satisfactory estimation of the case study.
The Bayesian method explained ensures a natural integration of knowledge from one source of information into the other, from in vitro to in vivo, making the best use out of our prior information and proper modelling of uncertainty. Many authors before us used plug-in estimates from the first stage of PK modelling without accounting for their uncertainty; we believe this may introduce an undue over-confidence in the model. Our generally applicable two-stage Bayesian approach is combining the benefits of one- and two-stage frequentist models. Therefore, it is an improvement of the current IVIVC methodology, where techniques based on averaged data and complex and potentially unstable mathematical deconvolution [7,8] are the standard.
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 Gaynor, C., Dunne, A., and Davis, J. (2009). The effects of averaging on accuracy of IVIVC model predictions. Journal of Pharmaceutical Sciences 98, 3829–3838.
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