Variance based global sensitivity analysis of physiologically based pharmacokinetic absorption models for BCS I-IV drugs

Developing Clinically Relevant Dissolution Specifications (CRDSs) for Oral Drug Products: Virtual Webinar Series

A webinar series that was organised by the Academy of Pharmaceutical Sciences Biopharmaceutics focus group in 2021 focused on the challenges of developing clinically relevant dissolution specifications (CRDSs) for oral drug products. Industrial scientists, together with regulatory and academic scientists, came together through a series of six webinars, to discuss progress in the field, emerging trends, and areas for continued collaboration and harmonisation. Each webinar also hosted a Q&A session where participants could discuss the shared topic and information. Although it was clear from the presentations and Q&A sessions that we continue to make progress in the field of CRDSs and the utility/success of PBBM, there is also a need to continue the momentum and dialogue between the industry and regulators. Five key areas were identified which require further discussion and harmonisation.

Evaluation of the Success of High-Throughput Physiologically Based Pharmacokinetic (HT-PBPK) Modeling Predictions to Inform Early Drug Discovery

Minimizing in vitro and in vivo testing in early drug discovery with the use of physiologically based pharmacokinetic (PBPK) modeling and machine learning (ML) approaches has the potential to reduce discovery cycle times and animal experimentation. However, the prediction success of such an approach has not been shown for a larger and diverse set of compounds representative of a lead optimization pipeline. In this study, the prediction success of the oral (PO) and intravenous (IV) pharmacokinetics (PK) parameters in rats was assessed using a “bottom-up” approach, combining in vitro and ML inputs with a PBPK model. More than 240 compounds for which all of the necessary inputs and PK data were available were used for this assessment. Different clearance scaling approaches were assessed, using hepatocyte intrinsic clearance and protein binding as inputs. In addition, a novel high-throughput PBPK (HT-PBPK) approach was evaluated to assess the scalability of PBPK predictions for a larger number of compounds in drug discovery. The results showed that bottom-up PBPK modeling was able to predict the rat IV and PO PK parameters for the majority of compounds within a 2- to 3-fold error range, using both direct scaling and dilution methods for clearance predictions. The use of only ML-predicted inputs from the structure did not perform well when using in vitro inputs, likely due to clearance miss predictions. The HT-PBPK approach produced comparable results to the full PBPK modeling approach but reduced the simulation time from hours to seconds. In conclusion, a bottom-up PBPK and HT-PBPK approach can successfully predict the PK parameters and guide early discovery by informing compound prioritization, provided that good in vitro assays are in place for key parameters such as clearance.

A Bayesian population physiologically based pharmacokinetic absorption modeling approach to support generic drug development: application to bupropion hydrochloride oral dosage forms

We propose a Bayesian population modeling and virtual bioequivalence assessment approach to establishing dissolution specifications for oral dosage forms. A generalizable semi-physiologically based pharmacokinetic absorption model with six gut segments and liver, connected to a two-compartment model of systemic disposition for bupropion hydrochloride oral dosage forms was developed. Prior information on model parameters for gut physiology, bupropion physicochemical properties, and drug product properties were obtained from the literature. The release of bupropion hydrochloride from immediate-, sustained- and extended-release oral dosage forms was described by a Weibull function. In vitro dissolution data were used to assign priors to the in vivo release properties of the three bupropion formulations. We applied global sensitivity analysis to identify the influential parameters for plasma bupropion concentrations and calibrated them. To quantify inter- and intra-individual variability, plasma concentration profiles in healthy volunteers that received the three dosage forms, each at two doses, were used. The calibrated model was in good agreement with both in vitro dissolution and in vivo exposure data. Markov Chain Monte Carlo samples from the joint posterior parameter distribution were used to simulate virtual crossover clinical trials for each formulation with distinct drug dissolution profiles. For each trial, an allowable range of dissolution parameters ("safe space") in which bioequivalence can be anticipated was established. These findings can be used to assure consistent product performance throughout the drug product life-cycle and to support manufacturing changes. Our framework provides a comprehensive approach to support decision-making in drug product development.

A latent variable approach to account for correlated inputs in global sensitivity analysis

In drug development decision-making is often supported through model-based methods, such as physiologically-based pharmacokinetics (PBPK). Global sensitivity analysis (GSA) is gaining use for quality assessment of model-informed inference. However, the inclusion and interpretation of correlated factors in GSA has proven an issue. Here we developed and evaluated a latent variable approach for dealing with correlated factors in GSA. An approach was developed that describes the correlation between two model inputs through the causal relationship of three independent factors: the latent variable and the unique variances of the two correlated parameters. The latent variable approach was applied to a set of algebraic models and a case from PBPK. Then, this method was compared to Sobol’s GSA assuming no correlations, Sobol’s GSA with groups and the Kucherenko approach. For the latent variable approach, GSA was performed with Sobol’s method. By using the latent variable approach, it is possible to devise a unique and easy interpretation of the sensitivity indices while maintaining the correlation between the factors. Compared methods either consider the parameters independent, group the dependent variables into one unique factor or present difficulties in the interpretation of the sensitivity indices. In situations where GSA is called upon to support model-informed decision-making, the latent variable approach offers a practical method, in terms of ease of implementation and interpretability, for applying GSA to models with correlated inputs that does not violate the independence assumption. Prerequisites and limitations of the approach are discussed.

The emerging role of physiologically-based pharmacokinetic/biopharmaceutics modeling in formulation development

Computer-based (in silico) modeling & simulation tools have been embraced in different fields of pharmaceutics for a variety of applications. Among these, physiologically-based pharmacokinetic/biopharmaceutics modeling (PBPK/PBBM) emerged as a particularly useful tool in formulation development. PBPK/PBBM facilitated strategies have been increasingly evaluated over the past few years, as demonstrated by several reports from the pharmaceutical industry, and a number of research and review papers on this subject. Also, the leading regulatory authorities have recently issued guidance on the use of PBPK modeling in formulation design. In silico PBPK models can comprise different dosing routes (oral, intraoral, parenteral, inhalation, ocular, dermal etc.), although the majority of published examples refer to modeling of oral drugs performance. In order to facilitate the use of PBPK modeling tools, a couple of companies have launched commercially available software such as GastroPlus™, Simcyp™ PBPK Simulator and PK-Sim®. This paper highlights various application fields of PBPK/PBBM modeling, along with the basic principles, advantages and limitations of this approach, and provides relevant examples to demonstrate the practical utility of modeling & simulation tools in different stages of formulation development.

Inter-compound and Intra-compound Global Sensitivity Analysis of a Physiological Model for Pulmonary Absorption of Inhaled Compounds

In recent years, global sensitivity analysis (GSA) has gained interest in physiologically based pharmacokinetics (PBPK) modelling and simulation from pharmaceutical industry, regulatory authorities, and academia. With the case study of an in-house PBPK model for inhaled compounds in rats, the aim of this work is to show how GSA can contribute in PBPK model development and daily use. We identified two types of GSA that differ in the aims and, thus, in the parameter variability: inter-compound and intra-compound GSA. The inter-compound GSA aims to understand which are the parameters that mostly influence the variability of the metrics of interest in the whole space of the drugs' properties, and thus, it is useful during the model development. On the other hand, the intra-compound GSA aims to highlight how much the uncertainty associated with the parameters of a given drug impacts the uncertainty in the model prediction and so, it is useful during routine PBPK use. In this work, inter-compound GSA highlighted that dissolution- and formulation-related parameters were mostly important for the prediction of the fraction absorbed, while the permeability is the most important parameter for lung AUC and MRT. Intra-compound GSA highlighted that, for all the considered compounds, the permeability was one of the most important parameters for lung AUC, MRT and plasma MRT, while the extraction ratio and the dose for the plasma AUC. GSA is a crucial instrument for the quality assessment of model-based inference; for this reason, we suggest its use during both PBPK model development and use.

Well-tempered MCMC simulations for population pharmacokinetic models

A full Bayesian statistical treatment of complex pharmacokinetic or pharmacodynamic models, in particular in a population context, gives access to powerful inference, including on model structure. Markov Chain Monte Carlo (MCMC) samplers are typically used to estimate the joint posterior parameter distribution of interest. Among MCMC samplers, the simulated tempering algorithm (TMCMC) has a number of advantages: it can sample from sharp multi-modal posteriors; it provides insight into identifiability issues useful for model simplification; it can be used to compute accurate Bayes factors for model choice; the simulated Markov chains mix quickly and have assured convergence in certain conditions. The main challenge when implementing this approach is to find an adequate scale of auxiliary inverse temperatures (perks) and associated scaling constants. We solved that problem by adaptive stochastic optimization and describe our implementation of TMCMC sampling in the GNU MCSim software. Once a grid of perks is obtained, it is easy to perform posterior-tempered MCMC sampling or likelihood-tempered MCMC (thermodynamic integration, which bridges the joint prior and the posterior parameter distributions, with assured convergence of a single sampling chain). We compare TMCMC to other samplers and demonstrate its efficient sampling of multi-modal posteriors and calculation of Bayes factors in two stylized case-studies and two realistic population pharmacokinetic inference problems, one of them involving a large PBPK model.

Considerations and Caveats when Applying Global Sensitivity Analysis Methods to Physiologically Based Pharmacokinetic Models

Three global sensitivity analysis (GSA) methods (Morris, Sobol and extended Sobol) are applied to a minimal physiologically based PK (mPBPK) model using three model drugs given orally, namely quinidine, alprazolam, and midazolam. We investigated how correlations among input parameters affect the determination of the key parameters influencing pharmacokinetic (PK) properties of general interest, i.e., the maximal plasma concentration (C_max) time at which C_max is reached (T_max), and area under plasma concentration (AUC). The influential parameters determined by the Morris and Sobol methods (suitable for independent model parameters) were compared to those determined by the extended Sobol method (which considers model parameter correlations). For the three drugs investigated, the Morris method was as informative as the Sobol method. The extended Sobol method identified different sets of influential parameters to Morris and Sobol. These methods overestimated the influence of volume of distribution at steady state (V_ss) on AUC24h for quinidine and alprazolam. They also underestimated the effect of volume of liver (V_liver) for all three drugs, the impact of enzyme intrinsic clearance of CYP2C9 and CYP2E1 for quinidine, and that of UGT1A4 abundance for midazolam. Our investigation showed that the interpretation of GSA results is not straightforward. Dismissing existing model parameter correlations, GSA methods such as Morris and Sobol can lead to biased determination of the key parameters for the selected outputs of interest. Decisions regarding parameters’ influence (or otherwise) should be made in light of available knowledge including the model assumptions, GSA method limitations, and inter-correlations between model parameters, particularly in complex models.