Experimental design and modelling approach to evaluate efficacy of β-lactam/β-lactamase inhibitor combinations

A β-lactamase inhibitor (BLI) confers susceptibility of β-lactamase-expressing multidrug resistant (MDR) organisms to the partnering β-lactam (BL).

To discuss the experimental design and modelling strategies for two-drug combinations, using ceftazidime- and aztreonam-avibactam combinations, as examples.

The information came from several publications on avibactam in vitro time-kill studies and corresponding pharmacodynamic models.

The experimental design to optimally gather crucial information from constant-concentration time-kill studies is to use an agile matrix of two-drug concentration combinations that cover 0.25- to 4-fold BL minimum inhibitory concentration (MIC) relative to the BLI concentrations to be tested against the particular isolate. This shifting agile design can save substantial costs and resources, without sacrificing crucial information needed for model development. The complex synergistic BL/BLI interaction is quantitatively explored using a semi-mechanistic pharmacokinetic-pharmacodynamic (PK/PD) mathematical model that accounts for antimicrobial activities in the combination, bacteria-mediated BL degradation and inhibition of BL degradation by BLI. A predictive mathematical formulation for the two-drug killing effects preserves the correlation between the model-derived EC₅₀ of BL and the BL MIC. The predictive value of PK/PD model is evaluated against external data that were not used for model development, including but not limited to in vitro hollow fibre and in vivo murine infection models.

As a framework for translational predictions, the goal of this modelling strategy is to significantly decrease the decision-making time by running clinical trial simulations with MIC-substituted EC₅₀ function for isolates of comparable susceptibility through established correlation between BL MIC and EC₅₀ values.