Biased computation of probability of target attainment for antimicrobial drugs

The medical literature is replete with articles in which there is confusion between “free concentration” and “unbound fraction” (f (u)), which is the ratio of free to total plasma concentration. The lack of clarity in distinguishing between these two terms has led to biased computations, erroneous interpretations, and misleading recommendations. The problems are highlighted in this paper, taking the example of calculation of Probability of Target Attainment (PTA). This metric is used to propose pharmacokinetic/pharmacodynamic (PK/PD) breakpoints required for the interpretation of Antimicrobial Susceptibility Testing. Based on Monte Carlo simulations of the PK/PD index, area under the unbound concentration time curve/minimum inhibitory concentration (fAUC/MIC), computation of PTA from total plasma concentrations scaled by f (u) ineluctably leads to biased estimates. The bias is greater if the variability associated with f (u) is added, instead of removing it during this scaling. The explanation for the bias is that total plasma drug concentrations are intrinsically more variable than the corresponding free concentrations. This is due to the variability of antimicrobial binding for total, but not for free plasma concentrations. In consequence, the greater variability always leads to underestimation of the PK/PD cutoff (i.e., the critical MIC that is guaranteed for a given percentile of the population). A further consequence is an increase in calculated dosage required to attain the targeted quantile. This erroneous approach, of using free antimicrobial drug fraction, is not limited to the derivation of PK/PD cutoff, but may also have consequences for antimicrobials drug safety in clinical patients.