2016 - Lisboa - Portugal

PAGE 2016: Methodology - New Modelling Approaches
Sebastian Wicha

A general pharmacodynamic interaction model based on the Bliss Independence criterion

Sebastian G. Wicha, Chunli Chen, Oskar Clewe and Ulrika S.H. Simonsson

Dept. of Pharmaceutical Biosciences, Uppsala University, Sweden

Objectives: Quantification of pharmacodynamic (PD) drug interactions is challenging. When reviewing current approaches, published PD interaction models [1] display several limitations: (i) evaluation of PD interactions is performed on observed effects instead of PD parameters and are often mono-dimensional; (ii) interaction models do not collapse to established additivity criteria; (iii) interaction parameters have no quantitative meaning and (iv) some models lack the possibility to capture more than two interacting drugs. The objective of the present work was to define a general PD interaction (GPDI) model overcoming all these limitations.

Methods: The Bliss Independence (BI) additivity criterion (EA,B=EA+EB-EAEB) was extended to quantify interactions in the GPDI model. Scaling was utilised to account for differences in Emax between drugs [2]. The interaction term was implemented as fractional change on the effect parameter (EC50 or slope or Emax) altering EA and/or EB in presence of the combination drug. The interactions between EA and EB were bi-directionally quantified by means of Emax models by INTAB and INTBA (maximum fractional change of the effect parameter) and EC50INT,AB and EC50INT,BA (interaction potencies). Interaction models for more than 2 drugs were also derived. Simulations and design explorations were performed in R (v 3.2.1).

Results: The GPDI model was successfully derived. For two drugs, four parameters quantified the possible interactions, but a reduced model with one interaction parameter was also derived. For INT=0, the GPDI model collapsed to BI (additivity), whereas for -1 < INT < 0 synergy and for INT > 0 antagonism was quantified. INT is to be interpreted as fractional change of drug potency/efficacy. Simulation studies displayed its flexibility and design explorations indicated identifiability of the GPDI model.  

Conclusion: The GPDI model allows for multi-dimensional quantification of PD interactions providing interpretable interaction parameters thereby being in accordance with the BI criterion. The model has been successfully used in pre-clinical studies of the combined effect of anti-tubercular drugs in in vitro and animal studies [3,4] and can be applied in both concentration-effect and longitudinal modelling activities. Application of the GPDI model in other settings and therapeutic areas with high prevalence of combination therapy seems promising. 

[1] D.M. Jonker, S.A.G. Visser, P.H. van der Graaf, R.A. Voskuyl, M. Danhof. Towards a mechanism-based  analysis of pharmacodynamic drug-drug interactions in vivo. Pharmacol. Ther., 106: 1–18 (2005).
[2] S.G. Wicha, M.G. Kees, J. Kuss, C. Kloft. Pharmacodynamic and response surface analysis of linezolid or vancomycin combined with meropenem against Staphylococcus aureus. Pharm Res, 32: 2410–2418 (2015).
[3] O Clewe, S.G. Wicha, C. de Vogel, J.E.M de Steenwinkel, U.S.H. Simonsson. Pre-clinical susceptibility characterization and pharmacodynamic interaction assessment using the multistate tuberculosis pharmacometric model.  25th PAGE Meeting, Lisbon (2016).
[4] C. Chen, S.G. Wicha, G.J. de Knegt, J.E.M. de Steenwinkel, U.S.H. Simonsson. Assessment of pharmacodynamic interactions in the mycobacteria tuberculosis infected mouse using the multistate tuberculosis pharmacometric model. 25th PAGE Meeting, Lisbon (2016). 

The research was funded by the Swedish Research Council and the Innovative Medicines Initiative Joint Undertaking (www.imi.europa.eu) under grant agreement n°115337, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution.

Reference: PAGE 25 (2016) Abstr 5946 [www.page-meeting.org/?abstract=5946]
Oral: Methodology - New Modelling Approaches
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