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Biased computation of Probability of Target Attainment for antimicrobial drugs

Toutain, Pierre-Louis; Pelligand, Ludovic; Gandia, Peggy; Ferran, Aude; Lees, Peter; Bousquet-Melou, Alain; Concordet, Didier


Pierre-Louis Toutain

Ludovic Pelligand

Peggy Gandia

Aude Ferran

Peter Lees

Alain Bousquet-Melou

Didier Concordet


The medical literature is replete with articles in which there is confusion between “free concentration” and “free fraction” (fu), 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 article, 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 (AST). Based on Monte Carlo simulations of the PK/PD index, fAUC/MIC, computation of PTA from total plasma concentrations scaled by fu, the unbound fraction, ineluctably leads to biased estimates. The bias is greater if the variability associated with fu is added, instead of removing it during this scaling. The explanation for the bias in critical values of low or high quantiles of f(back)AUC/MIC distributions (that is back computed fAUC/MIC) 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 PKPD cut-off 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 PKPD cutoff, but may also have consequences for safety antimicrobials in clinical subjects.


Toutain, P., Pelligand, L., Gandia, P., Ferran, A., Lees, P., Bousquet-Melou, A., & Concordet, D. (in press). Biased computation of Probability of Target Attainment for antimicrobial drugs. Clinical Pharmacology and Therapeutics,

Journal Article Type Article
Acceptance Date Jan 19, 2023
Deposit Date Jan 19, 2023
Publicly Available Date Apr 13, 2023
Journal Pharmacometrics & Systems Pharmacology.
Print ISSN 0009-9236
Publisher American Society for Clinical Pharmacology and Therapeutics
Peer Reviewed Peer Reviewed


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