The fractional maximal effect method: a new way to characterize the effect of antibiotic combinations and other nonlinear pharmacodynamic interactions

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Abstract
The checkerboard technique leading to the fractional inhibitory concentration indexes and the killing curve method are currently the most widely used methods to study antibiotic combinations. For both methods, experimental conditions and interpretation criteria are somewhat arbitrary. The relevance of the fractional inhibitory concentration index computation, in the classic case of additivity [P = d1/(D1)p + d2/(D2)p, where d1 and d2 are the doses of drugs 1 and 2 in combination to produce an effect at a percent level (P) and (D1)p and (D2)p are the doses required for the two respective drugs alone to produce the same effect] relies on the assumption of a linear relationship between the MIC and the concentration of the test antibiotics. In addition, there is no consensus as to the definition of synergy in killing curve interpretation. The fractional maximal effect (FME) method is a new approach which was developed to handle the nonlinear pharmacodynamics exhibited by antibiotics and other drugs. This method relies on the mathematical linearization of the nonlinear concentration-effect scales and eventual construction of an isobologram-type data plot. The FME method was applied to study interactions between several antibiotic combinations: amoxicillin and tetracycline, ciprofloxacin and erythromycin, and ticarcillin and tobramycin. These combinations were selected because the pharmacologic basis for their interactions has been previously described. The FME method correctly identified antagonism for the first two combinations and synergism for the last combination. Conclusions were reproducible across the range of concentrations studied. Besides providing information on the nature of the interaction, the method can rapidly explore the effect of changing concentration ratios of two antimicrobial agents on the degrees of interaction. The FME method may be applied to interactions between drugs or agents with either a linear or nonlinear endpoint measurement. Methods frequently used for drug combination testing are also discussed in the paper.