Development and evaluation of D-optimal 2x2 checkerboard designs for identification of pharmacodynamic drug interactions
Niklas Kroemer (1), Romain Aubry (2), Nicolas Gregoire (2), William Couet (2), Sebastian G. Wicha (1)
(1) Dept. of Clinical Pharmacy, Institute of Pharmacy, University of Hamburg, Hamburg, Germany; (2) Inserm U1070, University of Poitiers, Poitiers, France
Objectives: In pharmacodynamic (PD) interaction screening elucidation of the nature of the PD interaction (synergy, antagonism, additivity) is essential. Checkerboard assays are a common method for in vitro testing, but usually require many drug concentrations to be studied. The objective of the present study was to in silico develop a reduced optimal design to identify PD interactions accurately and efficiently to allow a high-throughput in vitro testing of antibiotic combinations.
Base for the estimation of parameters was the general pharmacodynamic interaction (GPDI) model [1], which not only identifies the interaction-type (synergy, antagonism, asymmetry), but also considers the directionality by identifying perpetrator and victim drugs.
Conventional schemes usually cover 9x9 tested combinations based on 2-fold increments of minimum inhibitory concentrations. An optimized design using 3x3 combinations based on effective concentrations (EC) was previously proposed, providing similar information as the conventional designs but being considerably more efficient [2]. In this study we developed further reduced designs with 2x2 combinations using D-optimal design strategies and performed an in vitro application against 12 bacterial strains.
Methods: Design optimization studies and evaluations were performed using the GPDI model implemented in ‘R’ [3]. For design development 1000 parameter sets of two fictive drugs A and B for each type of interaction were sampled. For each parameter set, the inverse value of the determinant of the Fisher information matrix was used as objective function to be minimized using the EC-parameters as design variables. Three different layouts (fixed rhombic design, free rhombic design, ray design) with four combination scenarios were optimized assuming effect addition (EA), Bliss Independence (BI) or Loewe Additivity (LA). All designs were evaluated using stochastic simulation and estimation (SSE), in which the accuracy and precision of the estimation of the interaction parameters and correct classification rates (CCR), assuming EA, BI or LA, were calculated and compared to reference designs. The fixed rhombic design developed assuming BI was applied in in vitro dynamic checkboard experiments [4] against ceftazidime-avibactam and fosfomycin. A BI-GPDI model was used to evaluate the in vitro data to identify PD drug interactions and estimate interaction parameters.
Results: The median of the EC parameter sets after optimization was defined to be the optimal design. Reference designs were a 3x3-design based on EC (EC20, EC50, EC80) [2], a conventional rich design with 9x9 standard 2-fold concentrations and a conventional sparse design with 3x3 standard 8-fold concentrations.. The designs developed assuming LA were nearly similar to the designs assuming BI (presented as EC-drug A:EC-drug B: fixed rhombic design: EC08[N1] :EC44, EC44:EC08, EC44:EC82, EC82:EC44; free rhombic design: EC06:EC53, EC53:EC06, EC39:EC80, EC81:EC40; ray design: EC14:EC46, EC21:EC70, EC46:EC15, EC68:EC22), the designs assuming EA tend to higher EC. Accuracy, precision and CCR in the SSE studies assuming the different additivity criteria were similar within the different designs, hence just the results for BI are shown: the conventional rich design led to the most precise and accurate estimates of interaction parameters and showed the highest CCR (rich: >97.0%; reduced: >83.9%; EC-3x3: >87.0%; fixed rhombic: >85.4%; free rhombic: >89.4%; ray: >84.7%). The 2x2 designs were less precise than the richer EC based design, but were more accurate and precise in estimation and classification than a simple reduction of a conventional design.[RA2] Application of a BI-GPDI model on in vitro fixed rhombic design experiments identified synergy for 10 strains, antagonism for one strain and an asymmetric interaction for another strain.
Conclusions: With more than halving the number of combination scenarios, the proposed checkerboard designs were less precise and accurate in the SSE, than the EC-3x3 reference, but the developed designs enabled estimation of interactions more precisely than a conventional checkerboard with similar number of concentrations. Although the reduced designs were less reliable as the EC-3x3 design, they provided information about the interaction type and in an in vitro application of the fixed rhombic design PD interactions in different strains could be estimated and quantified.
References:
[1] S. G. Wicha, C. Chen, O. Clewe, and U. S. H. Simonsson, “A general pharmacodynamic interaction model identifies perpetrators and victims in drug interactions,” Nat. Commun., vol. 8, no. 1, p. 2129, Dec. 2017, doi: 10.1038/s41467-017-01929-y.
[2] C. Chen, S. G. Wicha, R. Nordgren, and U. S. H. Simonsson, “Comparisons of Analysis Methods for Assessment of Pharmacodynamic Interactions Including Design Recommendations,” AAPS J., vol. 20, no. 4, p. 77, Jul. 2018, doi: 10.1208/s12248-018-0239-0.
[3] Team R Development Core, “A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, vol. 2. R Foundation for Statistical Computing, Vienna, Austria, p. https://www.R-project.org, 2018.
[4] S. G. Wicha, M. G. Kees, J. Kuss, and C. Kloft, “Pharmacodynamic and response surface analysis of linezolid or vancomycin combined with meropenem against Staphylococcus aureus,” Pharm. Res., vol. 32, no. 7, pp. 2410–2418, Jul. 2015, doi: 10.1007/s11095-015-1632-3.