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  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 . 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.
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Acknowledgement: 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.