Calculated using Cockcroft–Gault formula [28]. Creatinine clearance and serum albumin concentration determined on sample level, all other characteristics determined on patient level.

> This new reduced PK model was a two-compartment model with first-order elimination, interindividual variability on CL, V1 and V2, inter-occasion variability on CL, and a combined proportional and additive residual variability model (Supplementary Material S1, Figure S2). For this new reduced model, the PK parameters were re-estimated using the original dataset of the full model [30]. CL was shown to linearly increase with increasing CLCRCG up to an inflection point of 154 mL/min. An extensive internal model evaluation of the reduced model demonstrated high parameter accuracy and precision,

robustness and predictive performance and, thus, applicability of the PK model to the new population (Supplementary Material S1, Text and Figure S3).

In Figure 1, prediction errors are plotted against observed meropenem concentrations in the 34 ICU patients with full dosing history. The median prediction error across all observations was −1.2 mg/L, indicating a slight bias towards underprediction. The 50% prediction error interval ranging from −3.5 to +2.5 mg/L indicated acceptable precision for the ICU patient population the model was applied to with a single outlier (Figure 1). Other samples of the same patient showed acceptable prediction errors, and therefore, this sample was excluded from the subsequent NPDE analysis. While the overall NPDE distribution did not significantly differ from the standard normal distribution (global adjusted *p*-value: 0.0976), the Wilcoxon signed-rank test revealed a significant (*p*-value 0.0325) deviation from a mean of 0 and therefore confirmed a small bias (NPDE mean: 0.296; detailed results: Supplementary Material S1, Tables S2 and S3; Figure S4).

**Figure 1.** Absolute prediction error (mg/L) plotted against observed meropenem concentrations (n = 66) when predicting concentration based on the reduced pharmacokinetic model for the data in the subset. Points: median prediction error per sample. Colours: individual patients (i = 34). Error bar: 90% prediction interval of prediction error per sample. Solid horizontal line: median prediction error. Dashed line: 50% prediction interval of median prediction error. Dotted line: 90% prediction interval of median prediction error.

#### *3.2. Development of the Dosing Decision Tool*

#### 3.2.1. Selection and Evaluation of Dosing Regimens

Deterministic simulations demonstrated that 2000 mg loading doses provided little further benefit over 1000 mg loading doses, the latter being sufficient to reach minimum meropenem concentrations above minimum meropenem concentrations in steady state (Figure 2A). Furthermore, short-term (0.5 h) infusions were inferior to prolonged infusions (4 h) with short-term infusions generally having higher maximum and lower minimum concentrations for the same daily dose (Figure 2B). Consequently, dosing regimens with a 2000 mg loading dose and short-term infusions were not further considered for PTA analysis. PTA analysis of the 15 remaining dosing regimens (Table 1) showed that for prolonged (4 h) infusions, four-times-daily dosing (i.e., a 6 h dosing interval) reached higher PTA values with lower total daily doses than three-times-daily dosing (Table 3). Furthermore, four-times-daily dosing of prolonged infusions (4 h) reached higher PTA values than continuous infusions with the same total daily dose, which was due to the higher targets for continuous infusions (Table 3). For pathogens with MIC ≥ 8 mg/L in patients with augmented renal clearance (≥150 mL/min), none of the investigated dosing regimens reached a PTA ≥ 90%.

**Figure 2.** Predicted meropenem concentration–time profiles based on deterministic simulations using the reduced population pharmacokinetic model for a patient with creatinine clearance of 80.8 mL/min. (**A**) After either a 1000 (solid line) or a 2000 mg (dashed line) loading dose followed by prolonged (4 h) 1000 mg meropenem infusions with a dosing interval of 8 h. (**B**) After either a shortterm (0.5 h; dashed line) or a prolonged (4 h; solid line) 1000 mg meropenem infusion administered every 8 h.

**Table 3.** Probability of target attainment for different dosing regimens administered to a patient with a creatinine clearance according to Cockroft–Gault of 120 mL/min and infected by a pathogen with a minimum inhibitory concentration of 4 mg/L for meropenem.


Abbreviations: PI: Prolonged (4 h) infusion, CI: Continuous infusion.


Finally, dosing recommendations stratified by patient's CLCRCG and determined MIC were summarised in a single concise table (Figure 3).

**Figure 3.** Front page of the developed dosing decision tool for initial meropenem dosing in intensive care patients. Dosing recommendations are stratified for creatinine clearance according to Cockroft and Gault and target (minimal meropenem concentration or local pathogen-independent mean fraction of response (LPIFR), see text) MERO: meropenem; q6h: every 6 h dosing; q8h; every 8 h dosing; q12h: every 12 h dosing; PTA: probability of target attainment; MIC: minimal inhibitory concentration.

#### 3.2.2. Integration of Locally Available Pathogen Information

If the pathogen and its MIC value are not known at the time of dosing selection, two options are implemented in the dosing tool: an empirical dosing regimen based on non-species related EUCAST breakpoints for meropenem or a dosing regimen based on the LPIFR metric and pathogen-independent MIC distribution data from ICUs at Charité-Universitaetsmedizin Berlin. A short summary of both options was added on the backside of the dosing decision table (Supplementary Material S2). Compared to targeting the pathogen independent 'susceptible/susceptible at increased exposure' (2 mg/L) or the 'susceptible at increased exposure/resistant' (8 mg/L) EUCAST breakpoints, the LPIFR substantially reduced the drug exposure in patients while still assuring a desired percentage of 90% of patients being above the PK/PD target of 98%T>MIC. Based on the LPIFR, the daily dose for a patient with a creatinine clearance of 120 mL/min was 4000 mg, whereas there was a three-fold higher dose of 12,000 mg when targeting the EUCAST susceptible at increased exposure/resistant breakpoint (8 mg/L).

#### *3.3. Retrospective Evaluation of the Dosing Decision Tools Using Real Patient Data*

Of the 306 meropenem samples of the local study population, 46 (15.0%) were found to be below and 160 (52.3%) were found to be above the defined target range. The retrospective application of the developed tool recommended a change in dosing for the majority (77%) of patients with concentrations observed outside the target range (Figure 4). For 72% of the patients with minimum meropenem concentration below the target range, the developed

dosing tool recommended an increased daily dose, while for 78% of the patients with samples above the target range, a lower daily dose was recommended.

**Figure 4.** Frequency of daily meropenem dose adjustments by comparing the recommended daily dose to the actual administered daily dose at Charité-Universitaetsmedizin Berlin, stratified by non-attainment of the target range of the administered dosing regimen. Of 306 samples, 46 were below and 160 were above the target range.

#### **4. Discussion**

A concise dosing decision tool for initial meropenem dosing incorporating local susceptibility data was developed for the specific local needs. Additionally, a generalised workflow that can be used as blueprint for the development of such a dosing decision tool at the point-of-care was derived based on our experiences (Figure 5). After the identification of the elevated risk of inadequate antibiotic drug exposure in ICU patients, a local collaboration was established to assess and, if needed, improve antibiotic dosing. The close interprofessional collaboration between the antimicrobial stewardship (AMS) team, infectious disease specialists, critical care specialists, pharmacists, the clinical laboratory and pharmacometricians proved to be a vital part of the development process and should enable best adaptation to the local clinical routine. Bi-weekly meetings of the study team enabled continuous discussions, feedback, and adjustments throughout each step of the course of action.

As a mandatory prerequisite, the external PK model evaluation assured good predictive performance between the developed tool and the local patient population. The slight bias of the PK model to underpredict observed meropenem concentrations led to slightly lower PTA values for each dosing regimen and can be considered as an additional safety margin. The first evaluation of the dosing decision tool using retrospectively collected data suggests a substantial potential to improve target attainment. For 72% of the patients with concentrations below the target, a dose increase was recommended, and for 78% of the patients with concentrations above the target, a dose reduction was recommended. The suggested reduction of daily dose for 23% of samples below the target is due to the

recommendation of four-times-daily dosing instead of the three-times-daily dosing being administered: This more frequent administration of meropenem achieved higher PTA values despite reduced daily doses (Table 3). At the same time, the suggested increase in daily dose for 10% of the sample above the target range is mostly likely due to the selected PK model: The safety margin included in the PK model leads to more conservative, higher dosing recommendations to guarantee effective drug exposure. Additionally, in both cases, the high PK variability observed in critically ill patients renders a perfect recommendation for all patients untenable. To conclude, the retrospective evaluation highlighted the potential of the tool to improve meropenem therapy in critically ill patients. As next step, a prospective clinical trial should investigate the impact of the dosing decision tool on target attainment. The approach and workflow presented can improve acceptance and therefore the implementation of model-informed dosing decision tools at the point-of-care.

**Figure 5.** Steps (blue) considered in the generalised workflow development of a tabular precision dosing tool for initial therapy together with recommendations (yellow) to support each step.

All recommended dosing regimens included a 1000 mg loading dose to ensure an immediate achievement of sufficiently high meropenem concentrations at the start of antibiotic therapy. Regardless of the loading dose used (1000 mg vs. 2000 mg), the minimum meropenem concentration after the first maintenance dose was higher than or equal to minimum concentrations in steady state. Therefore, a 2000 mg loading dose showed no additional benefit compared to a 1000 mg loading dose and was considered to be an unnecessary higher drug exposure for patients and thus not retained in the dosing tool. Due to the different PK/PD targets for prolonged and continuous infusions, prolonged infusions provided higher target attainment for the same daily dose and as a consequence represent all integrated dosing regimen. In order to keep an explicit and clear structure in the dosing decision tool, only one dosing regimen was incorporated for each individual CLCRCG and MIC value. Overall, only six different initial dosing regimens (Table 2) were included in the dosing decision tool. This simplicity aims to achieve an initial dose individualisation to optimise dosing in ICU patients while maintaining a level of standardisation and avoiding complication of the ICU ward process. One further important note on the integrated dosing regimen: The dosing regimens selected and

integrated into the tool were selected based on their ability to reach a predefined PK target. As a consequence, high daily doses (up to 16 g) are included in the tool for high target concentrations. However, for such high targets, a change in antibiotic should be considered.

A further feature in the dosing decision tool is the use of local, hospital-specific and pathogen-independent MIC values. The LPIFR metric facilitates dosing based on not only patient characteristics but additionally on local bacterial susceptibility conditions in the hospital. While we foresee that this approach is a valuable opportunity to reduce unnecessary high meropenem dosing, we also strongly advise to apply it with caution: As local MIC distributions can vary over time, these need to be monitored and dosing suggestions based on LPIFR need to be updated regularly. Furthermore, in the rare event of a pathogen with high MIC values (>8–32 mg/L), the risk of target non-attainment could be underestimated until the MIC is determined. Therefore, it is vital to communicate those limitations to the decision-making team and encourage a dosing increase or change of antibiotic if higher MIC values are expected. In general, the dosing regimen recommendations based on the LPIFR metric should only be used as long as there is no further information about the pathogen (e.g., MIC) available. Furthermore, patients receiving renal replacement therapy (RRT), obese patients, and paediatric patients were not included in the PK model development and evaluation. Consequently, the derived dosing recommendations do not apply to those patient populations but only to adult critically ill patients.

For critically ill patients receiving antibiotics, drug measurements linked with Bayesian dosing software have been recommended for dose individualisation [3]. To date, this very promising approach could not always be implemented into clinical practice. Individualised meropenem therapy guided by concentration measurements is still only available in very few hospitals [10]. As an alternative, tabular dosing decision tools based on PTA analysis of an evaluated PK model can be used for initial dosing. Furthermore, these tabular dosing decision tools can provide dosing recommendations prior to the first drug measurement to improve dosing in this especially crucial time window of antibiotic drug therapy [31].

To optimise meropenem dosing, several complementary model-based tools or algorithms exist: the MeroRisk calculator supports the identification of critically ill patients at risk of suboptimal exposure and different model-based algorithms or nomograms provide dosing suggestions [30,32,33]. Unfortunately, none of the tools matched our local conditions and objectives: The dosing regimens frequently used at Charité-Universitaetsmedizin Berlin were either not included in the available tools or were part of a multitude of dosing regimen recommendations complicating the daily use of the tool. Furthermore, the risk of reaching toxic minimum concentrations was not considered in those other tools, and an evaluation of the underlying PK models would have been necessary. Most likely, this situation is similar for a wide range of drugs, model-based tools, and hospitals. Even when model-based tools or PK models are available for a specific drug in a specific patient population, the selected target or the clinical setting might hinder implementation and use. In those situations, local initiatives are needed to develop a dosing decision tool fit for the situation on site. As presented in our example, routine drug measurements can be used to evaluate published PK models instead of conducting expensive clinical trials to develop new PK models as the basis for new tools. Furthermore, by employing the LPIFR, antibiotic dosing prior to pathogen detection can be adapted to local susceptibility patterns. Even though tools developed to fit local conditions might be more difficult to transfer to other institutions, we believe the advantages of local initiatives clearly outweigh this drawback. The approach with the generalised workflow (Figure 5) may serve as a blueprint to a wide range of hospitals, patient populations, and drugs to develop a sophisticated dosing decision tool providing optimised initial dosing adapted for local conditions and objectives.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/pharmaceutics13122128/s1, Supplementary Material S1: Pharmacokinetic model selection, reduction and evaluation, Supplementary Material S2: Dosing decision tool.

**Author Contributions:** Conceptualisation: F.A.W., S.H., C.K., methodology: F.A.W., L.S., S.H., C.K.; software: F.A.W.; validation: F.A.W., formal analysis: F.A.W.; investigation F.A.W., M.S.S., A.T., F.P., S.H.; data curation: F.A.W., S.A.; writing—original draft preparation: F.A.W.; writing—review and editing: M.S.S., A.T., F.P., S.A., L.S., W.H., R.M., S.H., C.K.; visualisation: F.A.W.; supervision: C.K.; project administration: M.S.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** S.H. was partly supported by the Alexander von Humboldt Foundation, Germany, during this project.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Charité-Universitaetsmedizin Berlin (protocol code EA4/053/19, date of approval: 17 April 2019).

**Informed Consent Statement:** Patient consent was waived due to the retrospective evaluation of data from routine samples in the context of research without intervention.

**Data Availability Statement:** The data presented in the study are available at reasonable request from the corresponding author.

**Acknowledgments:** Lukas Duebel is acknowledged for support in data acquisition, Peggy Kiessling for laboratory support, Alexander Uhrig, and Ralf Lorenz for clinical support and Agata Mikolajewska for support of the study design. The authors thank the High-Performance Computing Service of ZEDAT at Freie Universitaet Berlin (https://www.fu-berlin.de/sites/high-performance-computing/ index.html, last accessed date: 1 December 2021) for high-performance computing capacities.

**Conflicts of Interest:** C.K. and W.H. report grants from an industry consortium (AbbVie Deutschland GmbH & Co. KG, AstraZeneca, Boehringer Ingelheim Pharma GmbH & Co. KG, Grünenthal GmbH, F. Hoffmann-La Roche Ltd., Merck KGaA and SANOFI) for the PharMetrX program. C.K. reports grants for the Innovative Medicines Initiative-Joint Undertaking ("DDMoRe"), Diurnal Ltd., the Federal Ministry of Education and Research within the Joint Programming Initiative on Antimicrobial Resistance Initiative (JPIAMR) and from the European Commission within in the Horizon 2020 framework programme ("FAIR"), all outside the submitted work.

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