Nicola Melillo (1), Adam S. Darwich (2), Maria Garcia-Cremades (3), Iñaki F. Troconiz (4), Leon Aarons (5), Amin Rostami-Hodjegan (5,6), Paolo Magni (1)
(1) Laboratory of Bioinformatics, Mathematical Modelling and Synthetic Biology, Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy; (2) Logistics and Informatics in Health Care, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), KTH Royal Institute of Technology, Stockholm, Sweden; (3) Department of Bioengineering and Therapeutic Sciences, UCSF, San Francisco, California, USA; (4) Pharmacometrics & Systems Pharmacology, Department of Chemistry and Pharmaceutical Technology, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain; (5) Centre for Applied Pharmacokinetic Research, Division of Pharmacy & Optometry, The University of Manchester, Stopford Building, Oxford Road, Manchester, United Kingdom; (6) Certara UK Limited, Simcyp Division, Sheffield, United Kingdom
Objectives
Physiologically based pharmacokinetic (PBPK) models are now routinely applied by the pharmaceutical industry throughout drug discovery, development and as part of regulatory submissions for informing the drug label [1–3].
Whilst efforts are made to harmonise the input data informing the PBPK models parameters, robustness of such inputs has not been uniform [3]. The ‘uncertainty in the parameter values‘ is not specific to PBPK and is a common issue for all mechanistic models regardless of parameters being derived from in vitro experiments or obtained by fitting in vivo observations. Moreover, when models are used in a population context, the parameters are variable as well as uncertain. If any parameter in these models, whether drug or system related, were uncertain or variable, then the model predictions would be naturally uncertain or variable. As highlighted by regulatory agencies, determining such uncertainties and variabilities is essential in building confidence in projections made by PBPK modelling [4]. This can be done using uncertainty analysis (UA) and global sensitivity analysis (GSA).
UA and GSA are recommended by practitioners from a plurality of disciplines [5], but, accordingly to our experience, they have historically been underused in PBPK. The aim of this work is to show, through different examples, the utility and most common pitfalls of UA and GSA for PBPK models.
Methods
UA refers to the quantification of the model output variation whilst GSA refers to the act of apportioning the output variation to the sources of variation in the model input parameters. To perform GSA, we used the variance based method [6], where two sensitivity indices are derived by decomposing the variance (V) of a model output Y. These indexes are between 0 and 1 and are known as the main effect Si and total effect STi. The higher Si and STi are, the more the i-th parameter explains V(Y) and so the more important it is, and vice versa [6].
Example 1) Understanding the model structure
The OrBiTo project (IMI), executed a large scale evaluation of the use of PBPK models to predict drug absorption, where the results showed high variability in performance [7–9]. In this context, we performed GSA on a PBPK model for drug absorption, with the aim of identifying key parameters that influence the oral bioavailability [10]. This analysis was done for drugs with various physicochemical characteristics belonging to the four classes of the Biopharmaceutics Classification System (BCS). Here, GSA was performed considering the between-drugs parameter variability. We called this approach inter-compound GSA.
Example 2) Assessing the confidence in the model predictions
We applied UA and GSA on a PBPK model for inhaled compounds in rats. Here, our aim was to quantify the uncertainties in the model predictions and to identify which were the most important parameters responsible for this uncertainty. Thus, GSA was performed considering the uncertainty in the parameter values. We called this approach intra-compound GSA [11].
Example 3) Understanding the most important covariates for a population
We used UA and GSA on a PBPK model for the anticancer drug gemcitabine (dFdC). The objective was to quantify the inter-individual variability of the dFdC active metabolite (dFdCTP) AUC in the tumour tissue for a population of patients and to understand what are the parameters that are mostly responsible for that. Here, GSA was performed considering the inter-individual variability in the parameters values [12].
Results
1) For the oral absorption model, the parameters of BCS I compounds that provided the most explanation of bioavailability were related to formulation properties and metabolism, for BCS II to dissolution and metabolism, for BCS III to permeability and formulation properties and for BCS IV to permeability and dissolution. In particular, the radius of the particle size of the formulation (r) was one of the most sensitive parameters at low dosage levels, with an ST>0.6 for all the BCS classes of neutral and acidic compounds at a dose of 0.1 mg and ST>0.65 for BCS II and BCS IV administered at a dose of 1 mg. In the OrBiTo database, r had a degree of missingness equal to 56.3% [8]. According to our study, a performance evaluation of PBPK models where r is fixed at an assumed value could result in an inaccurate interpretation [10].
2) By using the PBPK model for inhaled compounds, we performed in vitro to in vivo extrapolation for a drug belonging to the company Chiesi Farmaceutici. We used UA for quantifying the precision of the lung compartment AUC and MRT prediction, resulting in an uncertainty with a CV equal to 21% and 88%, respectively. For both the metrics, the passive permeability (P) was the most sensitive parameter, with a ST equal to 0.59 for the AUC and to 0.89 for the MRT. With the results of the UA, we concluded that the AUC prediction is relatively precise, while the MRT prediction is not. With the GSA results it was possible to understand that the only way to reduce the MRT uncertainty is to reduce the uncertainty in P [11].
3) Concerning the dFdC PBPK model, GSA showed that the concentration of two enzymes, dCK and CDA, is mainly responsible for the inter-individual variability of the dFdCTP AUC in tumour tissue (ST≈0.5 for both the parameters) [12]. These results are in agreement with the literature, where it is reported that dFdC clinical response can be related to the patients’ genotype [13].
There are some caveats when using GSA. In GSA is essential to consider correlations between the parameters, because, as we have shown, they can impact the analysis results. Nevertheless, no gold standard method is available for this situation. To cope with this issue, we expressed the correlations with functional relationships [14].
Conclusions
In this work, we showed how inter-compound GSA can be used to gain insight into the structure of PBPK models. This gives crucial information that helps us understand if a given parameter can be assumed, fixed or require further investigation to allow informed model predictions. This type of analysis can be valuable during model building. Intra-compound analysis instead allows the quantification of the confidence that can be given to the model predictions and, if they are considered unreliable, it helps in selecting what parameters should be further investigated to reduce this uncertainty. This type of analysis is useful during routinely PBPK use. Finally, GSA can help in understanding the parameters that mainly drive the inter-individual variability in a population, giving useful insight on the model behaviour. This can be useful for population PKPD models too.
As highlighted by regulatory agencies and practitioners from multiple disciplines, UA and GSA are crucial instruments for the quality assessment of model based inference [5]. Hence, we have the view that these techniques should be routinely applied in PBPK modelling and simulation.
References:
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[2] Jones HM, Chen Y, Gibson C, et al (2015) Physiologically based pharmacokinetic modeling in drug discovery and development: A pharmaceutical industry perspective. Clin Pharmacol Ther 97:247–262. https://doi.org/10.1002/cpt.37
[3] Jamei M (2016) Recent Advances in Development and Application of Physiologically-Based Pharmacokinetic (PBPK) Models: a Transition from Academic Curiosity to Regulatory Acceptance. Curr Pharmacol Rep 2:161–169. https://doi.org/10.1007/s40495-016-0059-9
[4] CHMP (EMA) (2018) Guideline on the reporting of physiologically based pharmacokinetic (PBPK) modelling and simulation. Committee for Medicinal Products for Human Use (CHMP), European Medicines Agency (EMA), London, UK
[5] Saltelli A, Guimaraes Pereira Â, Sluijs JPV der, Funtowicz S (2013) What do I make of your latinorum? Sensitivity auditing of mathematical modelling. Int J Foresight Innov Policy 9:213. https://doi.org/10.1504/IJFIP.2013.058610
[6] Saltelli A, Ratto M, Andres T, et al (2008) Global Sensitivity Analysis. The Primer. John Wiley & Sons, Ltd
[7] Margolskee A, Darwich AS, Pepin X, et al (2017) IMI – Oral biopharmaceutics tools project – Evaluation of bottom-up PBPK prediction success part 2: An introduction to the simulation exercise and overview of results. Eur J Pharm Sci 96:610–625. https://doi.org/10.1016/j.ejps.2016.10.036
[8] Margolskee A, Darwich AS, Pepin X, et al (2017) IMI – oral biopharmaceutics tools project – evaluation of bottom-up PBPK prediction success part 1: Characterisation of the OrBiTo database of compounds. Eur J Pharm Sci 96:598–609. https://doi.org/10.1016/j.ejps.2016.09.027
[9] Darwich AS, Margolskee A, Pepin X, et al (2017) IMI – Oral biopharmaceutics tools project – Evaluation of bottom-up PBPK prediction success part 3: Identifying gaps in system parameters by analysing In Silico performance across different compound classes. Eur J Pharm Sci 96:626–642. https://doi.org/10.1016/j.ejps.2016.09.037
[10] Melillo N, Aarons L, Magni P, Darwich AS (2019) Variance based global sensitivity analysis of physiologically based pharmacokinetic absorption models for BCS I–IV drugs. J Pharmacokinet Pharmacodyn 46:27–42. https://doi.org/10.1007/s10928-018-9615-8
[11] Melillo N, Grandoni S, Cesari N, et al (2019) Global sensitivity analysis of a physiologically based pulmonary absorption model. In: PAGE 28, Abstr 9072. Stockholm, Sweden. www.page-meeting.org/?abstract=9072
[12] Garcia-Cremades M, Melillo N, Troconiz IF, Magni P (2020) Mechanistic multi-scale pharmacokinetic model for the anticancer drug gemcitabine in pancreatic cancer. Clin Transl Sci. https://doi.org/10.1111/cts.12747
[13] de Sousa Cavalcante L, Monteiro G (2014) Gemcitabine: Metabolism and molecular mechanisms of action, sensitivity and chemoresistance in pancreatic cancer. Eur J Pharmacol 741:8–16. https://doi.org/10.1016/j.ejphar.2014.07.041
[14] Melillo N, Darwich AS, Magni P, Rostami-Hodjegan A (2019) Accounting for inter-correlation between enzyme abundance: a simulation study to assess implications on global sensitivity analysis within physiologically-based pharmacokinetics. J Pharmacokinet Pharmacodyn 46:137–154. https://doi.org/10.1007/s10928-019-09627-6
Reference: PAGE () Abstr 9363 [www.page-meeting.org/?abstract=9363]
Poster: Oral: Methodology - New Tools