*Article* **Development of a Model-Informed Dosing Tool to Optimise Initial Antibiotic Dosing—A Translational Example for Intensive Care Units**

**Ferdinand Anton Weinelt 1,2, Miriam Songa Stegemann 3,4, Anja Theloe 5, Frieder Pfäfflin 3,4, Stephan Achterberg 3, Lisa Schmitt 1,2, Wilhelm Huisinga 6, Robin Michelet 1, Stefanie Hennig 1,7,8 and Charlotte Kloft 1,\***


**Abstract:** The prevalence and mortality rates of severe infections are high in intensive care units (ICUs). At the same time, the high pharmacokinetic variability observed in ICU patients increases the risk of inadequate antibiotic drug exposure. Therefore, dosing tailored to specific patient characteristics has a high potential to improve outcomes in this vulnerable patient population. This study aimed to develop a tabular dosing decision tool for initial therapy of meropenem integrating hospitalspecific, thus far unexploited pathogen susceptibility information. An appropriate meropenem pharmacokinetic model was selected from the literature and evaluated using clinical data. Probability of target attainment (PTA) analysis was conducted for clinically interesting dosing regimens. To inform dosing prior to pathogen identification, the local pathogen-independent mean fraction of response (LPIFR) was calculated based on the observed minimum inhibitory concentrations distribution in the hospital. A simple, tabular, model-informed dosing decision tool was developed for initial meropenem therapy. Dosing recommendations achieving PTA > 90% or LPIFR > 90% for patients with different creatinine clearances were integrated. Based on the experiences during the development process, a generalised workflow for the development of tabular dosing decision tools was derived. The proposed workflow can support the development of model-informed dosing tools for initial therapy of various drugs and hospital-specific conditions.

**Keywords:** model-informed dosing tool; intensive care unit; antibiotic therapy; antimicrobial stewardship; meropenem; pathogen susceptibility

#### **1. Introduction**

Rational antibacterial therapy requires more than the appropriate choice of the antibiotic drug. Equally important are dosing regimens leading to an effective drug exposure linked to improved clinical success [1,2]. In intensive care unit (ICU) patients, the selection of an appropriate dosing regimen for an individual patient is challenging. The broad range of pathophysiological changes leads to high pharmacokinetic (PK) variability, which

**Citation:** Weinelt, F.A.; Stegemann, M.S.; Theloe, A.; Pfäfflin, F.; Achterberg, S.; Schmitt, L.; Huisinga, W.; Michelet, R.; Hennig, S.; Kloft, C. Development of a Model-Informed Dosing Tool to Optimise Initial Antibiotic Dosing—A Translational Example for Intensive Care Units. *Pharmaceutics* **2021**, *13*, 2128. https:// doi.org/10.3390/pharmaceutics 13122128

Academic Editors: José Martínez Lanao and Jonás Samuel Pérez-Blanco

Received: 3 October 2021 Accepted: 29 November 2021 Published: 10 December 2021

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results in substantial differences in drug exposures between patients receiving the same dosing regimen [3–7]. To address these challenges, drug concentration measurements in combination with model-informed Bayesian dosing software have been suggested to monitor and, if needed, adjust dosing in this patient [8,9]. Unfortunately, in many hospitals, reliable, timely, and frequent concentration measurements of antibiotic drugs other than aminoglycosides are not implemented, and the use of Bayesian dosing software to inform subsequent dose adaptation is not common [10,11]. The lack of specialist expertise and structured processes, the costs for software and bioanalysis, and inconsistent global, national, and local regulations (e.g., concerning liability) impede the widespread implementation of model-informed Bayesian dosing software [12]. If software-based tools and frequent concentration measurements are not feasible, one promising alternative to individualise antibiotic therapy is tabular model-informed dosing tools or algorithms. These dosing tools can provide adequate initial dosing regimens for a wide range of patients, based on their patient characteristics and PK models of the drugs. In this context, existing PK models could be leveraged for a local patient population to circumvent the need for further PK studies.

Commonly, at the start of antibiotic therapy, neither the pathogen nor its susceptibility to the antibiotic are known. In many cases, both remain unknown during the course of antibiotic therapy [13]. Thus, patients without determined pathogen and its susceptibility are empirically treated based on the reported PK/pharmacodynamics (PD) breakpoints of the suspected pathogens [14]. The timely initiation of adequate empiric therapy is associated with decreased mortality rates, decreased length of hospitalisation, and decreased health care costs in patients with severe infections [15]. However, this strategy does usually not utilise available knowledge of a hospital regarding the susceptibility of local pathogens, and thus, it accepts the risk of unnecessary high or low and possibly toxic or ineffective antibiotic concentrations.

Meropenem is a broad-spectrum antibiotic frequently used to treat severe infections in ICU patients. It is considered to be a safe and well-tolerated antibiotic drug [16]. However, changes in meropenem PK in chronic disease patients, such as chronic kidney disease, can increase the risk for ineffective or toxic meropenem exposure [17]. The antimicrobial activity of meropenem is linked to the time period of the unbound concentration exceeding the minimum inhibitory concentration (MIC) of a pathogen. Therefore, the PK/PD index is *f*T>MIC [18]. Recently, a concentration measurement program for beta-lactam antibiotics at selected ICUs of Charité-Universitaetsmedizin Berlin, a tertiary care centre with a total of >3000 in-patient beds, was initiated. Observational unpublished data from that program showed >60% of measured minimum meropenem concentrations outside the locally defined target range of one to five times MIC. Consequently, the main goal of the present study was to improve the initial meropenem therapy in ICU patients and to optimise antibiotic dosing prior to pathogen detection. Hence, this study (i) aims to develop a tabular model-informed dosing tool to optimise initial therapy of the antibiotic meropenem at Charité-Universitaetsmedizin Berlin and for this (ii) investigated how to integrate previously observed, yet unexploited local pathogen susceptibility information into dosing decisions. Ultimately, a generalised workflow for the development of tabular model-informed dosing decision tools for initial antibiotic therapy to foster their implementation at the point-of-care was developed.

#### **2. Materials and Methods**

#### *2.1. Patient Population and Meropenem Concentration Measurements*

For the development of the model-informed dosing tool, 306 routine blood samples, dosing information immediately prior to sampling, and patient-specific data of 81 ICU patients receiving meropenem therapy at two ICUs (Department of Infectious Diseases and Respiratory Medicine; Department of Surgery) at Charité-Universitaetsmedizin Berlin were collected (approval: Charité Ethics Committee, EA4/053/19). For a subset of 34 patients with 66 samples, the full dosing history was recorded.

Meropenem concentrations were determined by Labor Berlin (Labor Berlin—Charité Vivantes GmbH, Berlin). Samples were sent to the laboratory within 1 h, centrifuged, and stored at −20 ◦C until plasma meropenem concentrations were measured After protein precipitation with methanol, meropenem concentration was quantified using highperformance liquid chromatography (C8 reverse phase column and a 4 min step-elution gradient (0.2% HCOOH/MeOH)) coupled with tandem mass spectrometry (electrospray ionisation (ESI+) in multiple reaction monitoring). The used bioanalytical method was validated according to the protocol of the Society of Toxicological and Forensic Chemistry (GTFCh) showing good analytical performance (inaccuracy: <±5.9% relative error, imprecision: ≤6.3% coefficient of variation, calibration range: 2–30 μg/mL).

#### *2.2. Pharmacokinetic Model Selection, Reduction, and Evaluation*

Exclusively minimum meropenem concentrations and only 66 samples including the full dosing history were available. As a consequence, the PK data were unsuitable for PK model development. Instead, a published PK model was selected, evaluated for its appropriateness, and applied for the development of the dosing decision tool. The selection of the PK model was based on a high similarity of patient characteristics between the local study population and the model-underlying population.

To ensure the adequacy of the selected PK model for the new patient population, it was evaluated using median prediction errors and normalised prediction distribution errors (NPDEs) [19,20]. Model-predicted concentrations were obtained by 500 stochastic simulations based on the design and patient characteristics in the subset with full dosing history. To include parameter uncertainty, stochastic simulations were repeated for 1000 PK parameter sets obtained by bootstrapping of the dataset and re-estimation of the PK model. To assess possible deviations of the NPDEs from the standard normal distribution, the Wilcoxon signed-rank test (mean = 0), Fisher ratio test (variance = 1), and Shapiro– Wilks test (normality assumption) were used. Simulations and bootstrap analyses were performed using NONMEM 7.4.3 (ICON Development Solutions, Ellicott City, MD, USA) and PsN version 4.7.0) [21]. NPDEs were analysed using the npde package (v. 2.0) in R/Rstudio (v. 3.5.0/v. 1.1.447) [22].

#### *2.3. Pharmacokinetic/Pharmacodynamic Targets*

Based on current literature evidence, the PK/PD target for ICU patients receiving shorttime or prolonged meropenem infusions was defined as 100%*f*T>MIC, while for patients receiving continuous meropenem infusions, it was defined as 100%*f*T>4\*MIC to prevent steady-state meropenem concentrations within the mutant selection window [23,24]. The mutant selection window refers to a range of antibiotic drug concentrations in which only the growth of the most susceptible strains of a pathogen is suppressed. As a consequence, a growth advantage is provided to already available less susceptible strains in the pathogen population. Over a longer period of time, drug concentrations within the mutant selection window increase the proportion of less susceptible pathogens and thus the risk for resistant mutations to prevail [25]. Given that 100%*f*T>MIC cannot be achieved for an intravenous drug infusion on the first day of therapy, the attainment of a target of 98%*f*T>MIC was assessed. Total concentrations were evaluated due to the low (≈2%) protein binding of meropenem [26]. Furthermore, to assess target attainment based on a single observed minimum meropenem concentration and to limit toxicities arising from high minimum meropenem concentrations, an additional target was introduced: the target range for minimum plasma concentrations was defined to be 1–5xMIC [27].

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

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

Dosing regimens were preselected based on their feasibility to integrate into local clinical routine. To reduce the number of eligible dosing regimens emerging from the possible combinations of the four variables (loading dose, infusion dose, infusion dura-

tion, dosing interval), deterministic simulations were performed. Comparing the dosing regimens, those achieving higher predicted minimum meropenem concentrations were further considered. The remaining dosing regimens (Table 1) were evaluated for probability of target attainment (PTA); for each dosing regimen and patient, the meropenem concentration time profile was predicted 1000 times (Monte Carlo simulations), and the probability to attain the PK/PD target was calculated for each individual MIC value). PTA was computed for treatment days 1 and 2 across target concentrations values ranging from 1 to 32 mg/L and creatinine clearance values were estimated according to Cockcroft and Gault (CLCRCG) [28] ranging from 10 to 300 mL/min (10–150 mL/min in steps of 10 mL/min, above in steps of 50 mL/min). PK model parameter uncertainty was incorporated by repeating each Monte Carlo simulation and the respective PTA analysis 1000 times using the PK parameter sets obtained from a non-parametric bootstrap. A dosing regimen leading to a PTA ≥ 90% for the median of the 1000 computed PTA values was considered adequate [29]. All dosing regimens reaching a PTA ≥ 90% were further ranked according to higher probability of minimum concentrations being in the defined target range (1–5xMIC) and subsequently according to lower total daily dose. Thus, for each CRCLCG group and MIC value, a single dosing recommendation was derived.

**Table 1.** Meropenem dosing regimens investigated in probability of target attainment analysis for potential inclusion in the dosing decision tool.


All dosing regimens were administered in combination with a 1000 mg meropenem loading dose; *Grey*: Dosing regimen selected for the developed dosing tool.

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

As a high number of antibiotic therapies are initiated prior to pathogen detection, dosing recommendations accounting for this situation were developed. Based on the PTA results and the pathogen-independent MIC distribution observed at Charité-Universitaetsmedizin Berlin in the previous year, the local pathogen-independent mean fraction of response (LPIFR) was introduced as metric for each dosing regimen: To determine the LPIFR for a dosing regimen (*LPIFRDR*), first, the PTA for each investigated MIC level (*PTAMIC*,*DR*) was multiplied by the relative MIC frequency ( *nMIC NMIC*,*total* ; *nMIC* = number of MIC values observed at a MIC level, *NMIC*,*total* = total number of observed MIC values) at this level in the distribution of MIC values in patients treated at Charité-Universitaetsmedizin Berlin. Next, the resulting MIC-frequency weighted PTA values were summarised per dosing regimen (Equation (1)):

$$LPIFR\_{DR} = \sum\_{MIC} \left( PTA\_{MIC, DR} \times \frac{n\_{MIC}}{N\_{MIC, total}} \right). \tag{1}$$

An LPIFR of ≥90% was considered adequate. Within each CRCLCG group, dosing regimens with a LPIFR ≥ 90% were selected and ranked by lower total daily dose.

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

Prior to implementation into clinical practice, the developed dosing decision tool was evaluated using the observed local patient population. The total daily dose of the dosing regimens recommended by the dosing decision tool for the local study population was compared to the total daily dose of the actual administered dosing regimens. For this purpose, the dataset of the local study population was stratified based on target attainment (above, below, and in the defined target range of 1–5xMIC) and the administered and recommended daily dose were compared.

#### **3. Results**

#### *3.1. Pharmacokinetic Model Selection, Reduction, and Evaluation*

A PK model developed by Ehmann et al. was selected for evaluation based on the high similarity in patient characteristics between the population used for model development and the local study population (Table 2 and Supplementary Material S1, Figure S1) [30]. The two-compartment model included a piecewise linear relation between CLCRCG and clearance (CL), a power relation between body weight and the central volume of distribution (V1), and a linear relation between serum albumin concentration and the peripheral volume of distribution (V2). Of these three covariates, Ehmann et al. demonstrated that only CLCRCG had a clinically relevant impact on PTA [30]. Therefore, for the development of the dosing tool, CLCRCG was kept as the only covariate in the model.


**Table 2.** Overview of patient characteristics.
