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Abstract Background Beta-lactam antimicrobial concentrations are frequently suboptimal in critically ill patients. Population pharmacokinetic (PopPK) modeling is the golden standard to predict drug concentrations. However, currently available PopPK models often lack predictive accuracy, making them less suited to guide dosing regimen adaptations. Furthermore, many currently developed models for clinical applications often lack uncertainty quantification. We, therefore, aimed to develop machine learning (ML) models for the prediction of piperacillin plasma concentrations while also providing uncertainty quantification with the aim of clinical practice. Methods Blood samples for piperacillin analysis were prospectively collected from critically ill patients receiving continuous infusion of piperacillin/tazobactam. Interpretable ML models for the prediction of piperacillin concentrations were designed using CatBoost and Gaussian processes. Distribution-based Uncertainty Quantification was added to the CatBoost model using a proposed Quantile Ensemble method, useable for any model optimizing a quantile function. These models are subsequently evaluated using the distribution coverage error, a proposed interpretable uncertainty quantification calibration metric. Development and internal evaluation of the ML models were performed on the Ghent University Hospital database (752 piperacillin concentrations from 282 patients). Ensuing, ML models were compared with a published PopPK model on a database from the University Medical Centre of Groningen where a different dosing regimen is used (46 piperacillin concentrations from 15 patients.). Results The best performing model was the Catboost model with an RMSE and $$R^2$$ R 2 of 31.94–0.64 and 33.53–0.60 for internal evaluation with and without previous concentration. Furthermore, the results prove the added value of the proposed Quantile Ensemble model in providing clinically useful individualized uncertainty predictions and show the limits of homoscedastic methods like Gaussian Processes in clinical applications. Conclusions Our results show that ML models can consistently estimate piperacillin concentrations with acceptable and high predictive accuracy when identical dosing regimens as in the training data are used while providing highly relevant uncertainty predictions. However, generalization capabilities to other dosing schemes are limited. Notwithstanding, incorporating ML models in therapeutic drug monitoring programs seems definitely promising and the current work provides a basis for validating the model in clinical practice.

The surge in antimicrobial resistance and the limited availability of new antimicrobial drugs has fueled the interest in optimizing antibiotic dosing. An ideal dosing regimen leads to maximal bacterial cell kill, whilst minimizing the risk of toxicity or antimicrobial resistance. For beta-lactam antibiotics specifically, PK/PD-based considerations have led to the widespread adoption of prolonged infusion. The rationale behind prolonged infusion is increasing the percentage of time the beta-lactam antibiotic concentration remains above the minimal inhibitory concentration (%fT>MIC). The ultimate goal of prolonged infusion of beta-lactam antibiotics is to improve the outcome of infectious diseases. However, merely increasing target attainment (or the %fT>MIC) is unlikely to lead to improved clinical outcome for several reasons. First, the PK/PD index and target are dynamic entities. Changing the PK (as is the case if prolonged instead of intermittent infusion is used) will result in different PK/PD targets and even PK/PD indices necessary to obtain the same level of bacterial cell kill. Second, the minimal inhibitory concentration is not a good denominator to describe either the emergence of resistance or toxicity. Therefore, we believe a different approach to antibiotic dosing is necessary. In this perspective, we introduce the concept of the maximum tolerable dose (MTD). This MTD is the highest dose of an antimicrobial drug deemed safe for the patient. The goal of the MTD is to maximize bacterial cell kill and minimize the risk of antimicrobial resistance and toxicity. Unfortunately, data about what beta-lactam antibiotic levels are associated with toxicity and how beta-lactam antibiotic toxicity should be measured are limited. This perspective is, therefore, a plea to invest in research aimed at deciphering the dose–response relationship between beta-lactam antibiotic drug concentrations and toxicity. In this regard, we provide a theoretical approach of how increasing uremic toxin concentrations could be used as a quantifiable marker of beta-lactam antibiotic toxicity.